微積分
極限、導數、最優化與函數性質。
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the one - to - one functions g and h are defined as follows. $g = {(-4,…
\( g^{-1}(8)=-4 \) ### Part 2: Find \( h^{-1}(x) \)
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the one-to-one functions g and h are defined as follows. g={(-7, 9), (1…
s: - \( g^{-1}(7)=\boldsymbol{6} \) - \( h^{-1}(x)=\boldsymbol{\frac{x + 14}{3}} \) (or \( \boldsymbol{\frac{1}{3}x+\frac{14}{3}} \)) - \( (h^{-1}\circ h)(5)=\boldsymbol{5} \)
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(a) the graph of $y = f(x)$ is shown. draw the graph of $y = -f(x)$. (b…
### Part (a) # Explanation: ## Step 1: Understand the Transformation The transformation \( y = -f(x) \) is a reflection of the graph of \( y = f(x) \) over the \( x \)-axis. For e…
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the inverse of the following function? g(x)=6x+18
$g^{-1}(x)=\frac{1}{6}x - 3$
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given that $f(x)=\frac{4}{5}x + 9$, find the values of $x$ that produce…
If $f(x)=21$, then $x=15$ If $f(x)=1$, then $x=-10$ If $f(x)=13$, then $x=5$
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g(x) = \\frac{3}{4}x - 6\ g(-12) = \ g(0) = \ g(20) =
$g(-12)=-15$ $g(0)=-6$ $g(20)=9$
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label the corresponding number below with the value of the function at …
$f(-6)=39$ $f(2)=-1$ $f(5)=-16$
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6. the constitution specifically lists the powers of the federal govern…
This statement is related to the principle of **limited government** (or can be described as reflecting the enumeration of federal powers to restrict overreach, tied to constituti…
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definitions: a. the division of government into three branches: legisla…
E. A system that allows each branch of government to limit the powers of the other branches.
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objective: understand the foundational principles of the u.s. constitut…
1. B. The idea that the government derives its power from the consent of the governed. 2. D. The concept that the government must obey the law and cannot exercise powers beyond th…
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definitions: a. the division of government into three branches: legisla…
Since the question is not provided (only the definitions are given), it's impossible to determine the correct answer. Please provide the question (e.g., which term is being define…
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worksheet: principles of the u.s. constitution name: __________________…
To solve this matching problem about the principles of the U.S. Constitution, we first need to recall the definitions of each principle: 1. **Popular Sovereignty**: The government…
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hw 3.7: rational functions score: 6.5/28 answered: 7/28 question 8 find…
The horizontal asymptote of the function \(f(x)\) is \(y =-\frac{1}{5}\)
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hw 3.7: rational functions score: 5.5/28 answered: 6/28 question 7 for …
s: - For \(\frac{x^{2}+1}{x^{3}+2}\): Approaches \(0\) (horizontal asymptote \(y = 0\)) - For \(\frac{x^{3}+1}{x^{2}+2}\): Behaves like \(y=x\) (no horizontal asymptote, goes to \…
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function transformation if ((-1, 3)) is a point on the graph of (f(x)),…
\((-1, -1)\) (corresponding to the option \(\boldsymbol{(-1, -1)}\))
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question 5 let ( f(x) = 3 cdot \frac{3x^2 - 2x - 8}{4x^2 - 19x - 5} = 3…
\((-\infty, -\frac{1}{4}) \cup (-\frac{1}{4}, 5) \cup (5, \infty)\) ### 2) y - Intercept
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question 11 match the function with its graph. $f(x) = -2(x + 4)^2$
The graph with vertex at \((-4,0)\) and opening downward (the first graph in the top - left corner of the given set of graphs).
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a student likes watching television to relax but has to write a big pap…
D. Take a five - minute walk.
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the function ( f(x) ) is represented below as a graph. use ( f(x) ) to …
Blank #1: 5 Blank #2: -3
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a 25 - foot long ladder is propped against a wall at an angle of 18° wi…
B. 23.8 ft
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let $f(x) = 2x^3 + 15x^2 - 36x + 16$ be defined on $-7, 7$. find: a. th…
s: a. The absolute maximum is at the ordered pair \( \boldsymbol{(7, 1185)} \) b. The absolute minimum is at the ordered pair \( \boldsymbol{(1, -3)} \)
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find the exact location of the relative and absolute extrema of the fun…
- \( g(x) \) has an absolute minimum at \( (x,y) = (3, -32) \) - \( g(x) \) has an absolute maximum at \( (x,y) = (-3, 40) \) - \( g(x) \) has a relative minimum at \( (x,y) = (-1…
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find the limit. (in the limit, direct substitution applies? \\(\\lim_{x…
$0$
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consider the function $f(x) = 108x^{1/3} - 4x$ over the domain $0, 140$…
(Part a): Critical values are \( x = 0 \) (classified as a point where the derivative is undefined) and \( x = 27 \) (classified as a point where the derivative is zero). ### Part…
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the graph of the the function f(x) is shown at the right. a. make a tab…
### Part a: Table of Values for \( f(x) \) and \( f(x + 2) \) First, we analyze the graph of \( f(x) \). From the graph, we can determine the key points of \( f(x) \): - At \( x =…
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compositions of functions - the composition of functions is the process…
1. $f(g(x)) = -2x + 8$ 2. $(f \circ g)(x) = -12x - 8$ 3. $g(f(x)) = -2x - 1$ 4. $(g \circ f)(x) = -12x + 7$
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consider the rational function $f(x)=\frac{x^2 - 16}{x - 3}$, whose gra…
B. 4.5
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compute. 2 - 6 - 5
$-9$
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graph $y = 2x + 8$.
The line passes through points $(0, 8)$ and $(-4, 0)$, and extends infinitely in both directions along the grid.
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make a connection consider the graph of the equation $y = mx + b$. a. h…
a. Changing $m$ modifies the line's slope (steepness and direction): larger $|m|$ = steeper line; positive $m$ rises left-to-right, negative $m$ falls left-to-right; $m=0$ gives a…
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y = 10x + 50. a. graph the linear equation.
1. Plot the y-intercept at $(0, 50)$. 2. Plot a second point at $(1, 60)$ (using the slope of 10). 3. Draw a straight line through these two points, extending it across the visibl…
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f(x) = \\begin{cases} -x^2 + 4 & \\text{for } x \\leq 2 \\\\ 4x & \\tex…
The graph consists of: 1. A downward-opening parabola $f(x)=-x^2+4$ for $x\leq2$, with a closed endpoint at $(2, 0)$, passing through $(-2,0)$ and $(0,4)$. 2. A ray of the line $f…
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find (g ∘ f)(x). (g ∘ f)(x) = cot(-8x) choose the correct graph of (g ∘…
D. (The graph with vertical asymptotes spaced $\frac{\pi}{8}$ apart, where the curve increases between consecutive asymptotes)
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question 6, 6.5.47 part 2 of 4 hw score: 62.5%, 5 of 8 points points: 0…
$(f \circ g)(x) = -8\cot x$ Correct graph: A.
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find (f ∘ g)(x) and (g ∘ f)(x) and graph each of these functions. f(x) …
$\boldsymbol{-8\cot x}$
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question 24 $y = -2\\tan(4x - \\pi) - 1$, what is the period of this fu…
b. \( -\frac{\pi}{4} \) ### Second Question (Period of \( y = -2\tan(4x - \pi) - 1 \))
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question 22 $y = -2\\cos(4x + \\pi) - 1$, what is the period of this fu…
a. 2 ### Second Question (Period)
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question 6 consider the function $f(x)=x^2 - 6x + 3$ graph $f(x)$ what …
- Vertex of $f$: $(3, -6)$ - Equation of the line of symmetry: $x=3$ - $f$ has a minimum of $-6$ - The $x$-intercept(s) of $f$ is/are: $(0.55, 0)$ and $(5.45, 0)$ - The $y$-interc…
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the graph of a function is given below. give all x-intercepts and y-int…
(a) \(x\) - intercept(s): \(2\) (b) \(y\) - intercept(s): \(1\) Wait, no, after re - examining the graph, the correct x - intercept is \(2\) (since the graph crosses the x - axis …
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which of the following statements about google photos is false? it can …
The statement "Integration with Facebook and Instagram allows users to add their favorite photos to these social networks with one tap" is false. So the answer is the option with …
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fractions worksheet find the sum. 1. $4\\frac{5}{6} + \\frac{4}{5} =$ 2…
1. $5\frac{19}{30}$ 2. $8\frac{2}{3}$ 3. $4\frac{1}{8}$ 4. $1\frac{17}{20}$ 5. $7\frac{46}{55}$ 6. $1\frac{13}{20}$ 7. $9\frac{2}{63}$ 8. $6\frac{7}{9}$ 9. $9\frac{5}{22}$ 10. $7\…
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if $p(x) = 3x^2 - 2x + 1$, find $p(-4)$.
57
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write the function with the given transformation from the given parent …
$f(x) = -5\sqrt[3]{x} + 7$
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determine whether each description best refers to a sole proprietorship…
To solve this, we analyze each description based on the characteristics of sole proprietorship, partnership, corporation, and LLC: ### Part a - A corporation is a separate legal e…
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f(x) = 8(x - 4)^{2/3} + 8. (a) find the interval(s) where f(x) is incre…
To solve the problem, we analyze the function \( f(x) = 8(x - 4)^{2/3} + 8 \) by examining its derivative. ### Step 1: Find the derivative of \( f(x) \) We use the chain rule. Let…
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use transformations to graph the function. $f(x) = -3|x + 2| - 4$
The graph of $f(x)=-3|x+2|-4$ is a downward-opening V-shape with vertex at $(-2, -4)$, passing through points like $(-1, -7)$, $(-3, -7)$, $(0, -10)$, $(-4, -10)$, and extending i…
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is the function k(x) even, odd, or neither?
The function $k(x)$ is even.
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graph the function. $r(x)=\\begin{cases} x^2 - 1 & \\text{for } x \\leq…
The graph consists of: 1. The left portion: the parabola $y = x^2 - 1$ for all $x \leq 1$, with a closed point at $(1, 0)$. 2. The right portion: the straight line $y = 5x - 5$ fo…
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find the derivative of $f(x) = -5x^2log_7(2x^4 + 13)$.\ \ $\\boldsymbol…
$f'(x)= - 10x\log_{7}(2x^{4}+13)-\frac{40x^{5}}{(2x^{4}+13)\ln7}$ (the third option)
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follow the seven step strategy to graph the following rational function…
For \( x = -7 \), \( f(x)=-\frac{49}{45} \); for \( x = -6 \), \( f(x)=-\frac{21}{16} \); for \( x = -1 \), \( f(x)=\frac{7}{3} \); for \( x = 1 \), \( f(x)=-\frac{7}{3} \); for \…
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on a piece of paper, graph this system of inequalities. then determine …
D. Region A
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use transformations to graph the function. $l(x)=-sqrt{-x}-6$
The graph of $L(x)=-\sqrt{-x}-6$ is obtained by: 1. Reflecting $y=\sqrt{x}$ over the y-axis, 2. Reflecting the result over the x-axis, 3. Shifting the final graph down 6 units. Ke…
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use the graph $y = f(x)$ to graph the given function. $y = \\frac{1}{7}…
The graph of $y=\frac{1}{7}f(x)$ is a vertical compression of $y=f(x)$ by a factor of $\frac{1}{7}$, with vertices at $(-7, 0)$, $(0, 1)$, and $(7, 0)$, connected by straight line…
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solve \\(ln 5 + ln 2x = 3\\). (1 point) \\(\\bigcirc\\) \\(x = \\dfrac{…
\(x=\frac{e^{3}}{10}\) (corresponding to the option with \(x = \frac{e^{3}}{10}\))
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which domain window settings would be appropriate if you wanted to grap…
Xmin $= -\pi$ Xmax $= 3\pi$
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click to select points on the graph. $y = -x - 1$ $y = -\frac{3}{5}x + …
1
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is the function t(x) even, odd, or neither? even odd neither
neither
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use transformations to graph the function. $m(x)=3\\sqrt{x + 2}-3$
The graph of $m(x)=3\sqrt{x+2}-3$ is the parent square root function shifted left 2 units, vertically stretched by a factor of 3, and shifted down 3 units. Key points to plot are …
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trazar la recta. $y = -\\frac{3}{2}x - 3$
To draw the line \(y =-\frac{3}{2}x-3\), plot the points \((0, - 3)\), \((2,-6)\) (or \((-2,0)\)) and draw a straight line through them.
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use transformations to graph the function.\ \\( n(x) = 3|x| \\)
The provided graph correctly represents $n(x)=3|x|$ as it is a vertical stretch of the parent absolute value function $f(x)=|x|$ by a factor of 3, with key points $(0,0)$, $(2,6)$…
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use translations to graph the given function. $d(x)=\\frac{1}{x + 2}-3$
The graph of $d(x)=\frac{1}{x+2}-3$ is the parent function $f(x)=\frac{1}{x}$ shifted left 2 units and down 3 units, with vertical asymptote $x=-2$ and horizontal asymptote $y=-3$…
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question 3 of 10 if $f(x) = 3x^2$ and $g(x) = x + 2$, find $(f \\bullet…
D. \( 3x^3 + 6x^2 \)
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Question was provided via image upload.
$3$
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look at this graph: what is the minimum value of this function?
0
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there were 74 ice pops in a freezer. david put additional ice pops in t…
22
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find the intercepts and use them to graph the equation. y=2x+4 select t…
A. The intercept(s) is/are $(-2, 0), (0, 4)$ To graph the line, plot the points $(-2, 0)$ and $(0, 4)$, then draw a straight line connecting them.
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let $f(x) = \\frac{1}{x - 2}$ and $g(x) = 2x + 5$. then $(f \\circ g)(2…
$(f \circ g)(2) = \frac{1}{7}$ $(f \circ g)(x) = \frac{1}{2x+3}$
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given that $f(x) = 2x - 8$ and $g(x) = 2 - x^2$, calculate (a) $f(g(0))…
(a) $-4$ (b) $-62$
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if $f(x) = x^2 + 3$, $g(x) = x - 2$, and $h(x) = \\sqrt{x}$, then $(f \…
$(f \circ g)(x) = x^2 -4x +7$ $(g \circ f)(x) = x^2 +1$ $(h \circ g)(x) = \sqrt{x-2}$
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let $f(x) = \\sqrt{x}$ and $g(x) = \\frac{1}{x + 4}$. find the composit…
$\frac{1}{\sqrt{x+4}}$ (or equivalently $\sqrt{\frac{1}{x+4}}$)
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let $f(x) = x^2 e^{9x}$. (a) find the critical values of $f(x)$. if the…
\( -\frac{2}{9}, 0 \) ### Part (b): Intervals where \( f(x) \) is increasing
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in each part that follows, you are given an equation of a line and a po…
(a) $\boldsymbol{y = -\frac{1}{8}x}$ (b) $\boldsymbol{y = -\frac{1}{5}x + \frac{16}{5}}$
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given the function $f(x) = 2x^2 + 7x - 2$. calculate the following valu…
$f(0)=-2$ $f(2)=20$ $f(-2)=-8$ $f(x+1)=2x^2+11x+7$ $f(-x)=2x^2-7x-2$
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given the function $f(x) = 4x^2 - 5x + 4$. calculate the following valu…
$f(-2)=30$ $f(-1)=13$ $f(0)=4$ $f(1)=3$ $f(2)=10$
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the plot below represents the function $f(x)$ evaluate $f(1)$ $f(1) = $…
$2$
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if $f(-10) = -2$, then the point \\boxed{} is on the graph of $f$. ques…
$(-10, -2)$
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the plot below represents the function $f(x)$: evaluate $f(4)$: $f(4) =…
$f(4) = 1$ $x = 2$
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the plot below represents the function $f(x)$: evaluate $f(4)$: $f(4) =…
$f(4) = 2$ $x = -2$
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question 28 of 50 divide. 13.3 ÷ 0.7 question 29 of 50 david’s annual s…
19 ### Question 29
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for the last 6 days, chiang worked 4.9 hours each day. how many hours d…
0.6 ### Question 24
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attempt 1; 10 attempts remaining. the function \\( f(x) = -6x^3 + 36x^2…
- The function is increasing on the interval \( \boldsymbol{(1, 3)} \). - It is decreasing on the interval \( \boldsymbol{(-\infty, 1)} \) and the interval \( \boldsymbol{(3, \inf…
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produce a rule for the function whose graph is shown. (hint: consider u…
$$ f(x)= \begin{cases} -\dfrac{1}{4}x^2 & \text{for } x < 3 \\ 2 & \text{for } x \geq 3 \end{cases} $$
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produce a rule for the function whose graph is shown. (hint: consider u…
$$ f(x)= \begin{cases} -\sqrt{x} & \text{for } x < 3 \\ 2 & \text{for } x \geq 3 \end{cases} $$
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6.2 symmetry and piecewise - defined functions question 12 of 15 (4 poi…
leftmost, $(1, 0)$
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r(x) = \\begin{cases} x^2 - 1 & \\text{for } x \\leq 1 \\\\ 5x - 5 & \\…
Slope: $5$, y-intercept: $(0, -5)$
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graph the function.\\( r(x) = \\begin{cases} x^2 - 1 & \\text{for } x \…
The solid dot is at $(1, 0)$
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graph the function. $r(x) = \\begin{cases} \\ \\ x^2 - 1\\ \\text{ for …
quadratic function (parabola); $(0, -1)$
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part: 0 / 3 (a) graph ( a(x) = -2x ) for ( x < 1 ). (b) graph ( b(x) = …
(a) For $a(x)=-2x$ ($x<1$): A downward-sloping line passing through $(0,0)$, $(-1,2)$, with an open circle at $(1,-2)$, extending left infinitely. (b) For $b(x)=\sqrt{x-1}$ ($x\ge…
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match the function with its graph. ( f(x) = x + 1 ) for ( x < 3 )
The correct graph is the **topmost graph** (first option, with closed dot at $(0,1)$, open dot at $(3,4)$, and rising line extending left from $(0,1)$).
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a sled accelerates down a hill and then slows down after it reaches a f…
- The speed of the sled is 20 ft/sec after 10 sec. - The speed of the sled is 40 ft/sec after 20 sec. - The speed of the sled is 4.5 ft/sec after 30 sec. - The speed of the sled i…
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6.2 symmetry and piecewise - defined functions question 6 of 15 (4 poin…
3
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evaluate the function for the given values of x. $f(x) = \\begin{cases}…
$f(0)=2$ $f(-2)=17$
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part 2 of 4 (b) find -k(x). -k(x) = -8x³ - 3x part 3 of 4 (c) is k(-x) …
(c) $k(-x) = -k(x)$ (d) odd
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question 3 of 15 (4 points) | question attempt: 1 of unlimited (a) give…
(a) $6x^2 + 2|x|$ (b) Yes, $f(-x)=f(x)$ (c) Even
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use the graph to determine whether the function is even, odd, or neithe…
The function is even.
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what type of symmetry does an even function have? even functions have s…
y-axis (vertical axis)
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use transformations to graph the function. ( v(x) = -(x - 5)^2 - 3 ) pa…
1. Shift the graph of $f(x)=x^2$ 5 units to the right 2. Reflect the resulting graph over the x-axis 3. Shift the resulting graph 3 units downward
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measures of development for selected countries, 2017 | country | gross …
E. All the statistics aggregate data to the country level. Frequently, there is a great deal of variation in development within countries that is hidden by aggregated data.
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write an exponential function for the graph. write the function in the …
\( y = 2(2)^x \) (or \( y = 2^{x + 1}\), but in the form \( y=a(b)^x \), it is \( y = 2(2)^x \))
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s the graph of $f(x)=sqrt{x}$. form it to make it as the graph of $g(x)…
The graph of $g(x)=\sqrt{x+1}-3$ is the graph of $f(x)=\sqrt{x}$ shifted **1 unit to the left** and **3 units down**. Its key points include $(-1,-3)$, $(0,-2)$, and $(3,-1)$, and…