微积分
极限、导数、最优化与函数性质。
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homework assignment 3.3: power functions and polyno score: 9/10 answere…
2
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5. the graph of a function is a line that passes through the points (0,…
$y=3x+1$
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homework assignment 3.3: power functions and polyno score: 7/10 answere…
5
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consider the polynomial function $f(x) = -9x - 6x^2 + x^7 + 5x^9$. as $…
s: As \( x\to -\infty \), \( f(x)\to\boldsymbol{-\infty} \) As \( x\to\infty \), \( f(x)\to\boldsymbol{\infty} \)
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consider the polynomial function $f(p) = -p^8 - 2p^7 + 4p^6 - 5$. as $p…
As \( p \to -\infty \), \( f(p) \to \boldsymbol{-\infty} \) As \( p \to \infty \), \( f(p) \to \boldsymbol{-\infty} \)
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3. lacey and richens each have a personal function machine. lacey’s mac…
a. $L(x) = x^2 - 1$, $R(x) = 3(x + 2)$ b. 30 c. Yes, it changes the output. The composite functions $R(L(x)) = 3x^2 + 3$ and $L(R(x)) = 9x^2 + 36x + 35$ are not equivalent, and te…
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question the table below represents a linear function. identify the slo…
\(\frac{7}{4}\)
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describe the long run behavior of $f(n) = 5n^9 - n^5 - 5n^3 + 4$ as $n …
As \( n ightarrow-\infty \), \( f(n) ightarrow-\infty \); As \( n ightarrow\infty \), \( f(n) ightarrow\infty \)
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describe the long run behavior of $f(x) = -x^7$ as $x \\to -\\infty$, $…
As \(x \to -\infty\), \(f(x) \to \infty\) As \(x \to \infty\), \(f(x) \to -\infty\)
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question what is the rate of change of the function $y = 3x + 3$?
The rate of change of the function \(y = 3x+3\) is \(3\).
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describe the end behavior (long run behavior) of $f(x)=x^2$ as $x\\to -…
As \( x \to -\infty \), \( f(x) \to \infty \) As \( x \to \infty \), \( f(x) \to \infty \)
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the table below represents a linear function. identify the rate of chan…
\(\frac{5}{4}\)
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graph the function. $y = \\frac{9}{2}\\sqrt3{x}$
To graph \( y=\frac{9}{2}\sqrt[3]{x} \), follow these steps: 1. Identify key points by substituting \( x=-8,-1,0,1,8 \) (and other values if needed) into the function to get \((-8…
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2-variable linear inequality a $y > \\frac{3}{2}x + 3$ b $y \\geq \\fra…
### First, determine the inequality from the graph: ## Step1: Analyze the line The line has a slope of $\frac{3}{2}$ (rise over run: from $(0,3)$ to $(2,6)$? Wait, no, from $(0,3)…
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#1-9 count the slope using the two points on the line. *all answers in …
1) $\frac{7}{5}$ 2) $-\frac{1}{4}$ 3) $-\frac{3}{5}$ 4) $-\frac{4}{3}$ 5) $2$ 6) $-\frac{1}{4}$ 7) $\frac{1}{2}$ 8) $-1$ 9) $-1$
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question 4 of 10 what constitutes a disability? impairment activity lim…
All of the Above
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2-variable linear inequality which linear inequality graphs the solutio…
B. \(y\geq\frac{3}{2}x + 3\)
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graph the function. $y = 4\\sqrt3{x}$
To graph \( y = 4\sqrt[3]{x} \), we can analyze key points and the shape of the cube - root function: ### Step 1: Recall the parent function The parent function of a cube - root f…
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graph the function. $y = \\sqrt3{x} + 1$
To graph \( y=\sqrt[3]{x + 1} \), follow these steps: 1. **Identify Transformation**: The function is a horizontal shift of \( y = \sqrt[3]{x} \) 1 unit to the left. 2. **Find Key…
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graph the function. $y = \\frac{3}{2}\\sqrt3{x}$
To graph \( y = \frac{3}{2}\sqrt[3]{x} \), we: 1. Recognize it's a vertical stretch (\( \frac{3}{2} \) factor) of \( y=\sqrt[3]{x} \). 2. Find key points using the function: - Whe…
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the height ( y ) (in feet) of a ball thrown by a child is ( y = -\frac{…
5 ### Part (b)
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suppose that the functions q and r are defined as follows. q(x) = x² + …
$(q \circ r)(1)=16$ $(r \circ q)(1)=4$
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suppose that the functions p and q are defined as follows. p(x)=x+1 q(x…
$(q\circ p)(4)=49$ $(p\circ q)(4)=32$
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suppose that the functions p and q are defined as follows. p(x)=2x+3 q(…
$(p \circ q)(-3) = -33$ $(q \circ p)(-3) = -18$
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$\\sqrt{-15}$ $\\sqrt{-15}=\\square$ (simplify your answer. type your a…
$0+\sqrt{15}i$
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consider the function $g(x)=x^2 + 8x + 18$ graph $g(x)$ what is the ver…
s: - Vertex of \( g \): \((-4, 2)\) - Equation of the line of symmetry of \( g \): \( x=-4 \) - \( g \) has a minimum of \( 2 \) - The \( x \)-intercept(s) of \( g \): DNE - The \…
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graph $g(x) = -3x^2 - 12x - 14$.
To graph \( g(x) = -3x^2 - 12x - 14 \): 1. **Vertex**: \((-2, -2)\) (from vertex form \( g(x) = -3(x + 2)^2 - 2 \)). 2. **Direction**: Opens downward (since the coefficient of \( …
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graph $g(x) = 4(x + 4)^2 - 2$.
To graph \( g(x) = 4(x + 4)^2 - 2 \): 1. Plot the vertex at \( (-4, -2) \). 2. Since \( a = 4 > 0 \), the parabola opens upward. 3. Use the narrow width (due to \( |a| = 4 > 1 \))…
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le for finding the domain and range of a function graphically ______ → …
1. Domain → Inputs; Found along the \( \boldsymbol{x} \) axis (left to right) 2. Range → Outputs; Found along the \( \boldsymbol{y} \) axis (bottom to top)
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write 9.5 × 10² in standard form. enter your answer as an integer or de…
950
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homework assignment 3.2: quadratic functions score: 0/10 answered: 0/10…
\(y=\frac{8}{9}(x - 3)^2-2\) (or other equivalent forms like standard form \(y=\frac{8}{9}x^2-\frac{16}{3}x + 6\))
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finding slope #1 (graphing method) graph the points and find slope usin…
\(\frac{1}{4}\) ### Problem 2:
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unit 1.2 functions and graphs day 2 notes date:__________ domain and ra…
- First blank: input - Second blank: \(x\) - Third blank: input values (or \(x\)-values) - Fourth blank: output values (or \(y\)-values)
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what is the y - value of this function when x = -9?
\(-0.7\) (or \(-\frac{7}{10}\))
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question determine if the function below has a horizontal or a slant as…
The slant asymptote is \(y = 3x - 5\), so as \(x\) approaches infinity (positive or negative), \(y\) approaches \(3x - 5\). If we consider the linear part (the slant asymptote), t…
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i was born in a little town called hope, arkansas... i remember that ol…
B. He talked about hope and the American dream. C. He talked about growing up in a family that didn't have much money.
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The vertical asymptotes are \(x = 0\) and \(x=-2\)
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directions: read each problem and answer carefully. explain your work. …
1. (Graph: $f(x)=(x-1)^3-2$ plotted with key points $(-1,-10), (0,-3), (1,-2), (2,-1)$; inverse $y=\sqrt[3]{x+2}+1$ plotted with reflected points $(-10,-1), (-3,0), (-2,1), (-1,2)…
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
There are no vertical asymptotes.
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The function \( f(x)=\frac{x^{2}-2x - 15}{3x - 15} \) has no vertical asymptotes (it has a hole at \( x = 5 \)).
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25. 6 + 3²(5 - √4)
33
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*23. 0.014 ÷ 0.5 answer:
0.028
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no calculators 11.) sketch the following below each equation, then desc…
s (Descriptions of Transformations): - \( y = x^2 \): Parent parabola, vertex \((0,0)\), no transformations. - \( y = x^2 + 2 \): Vertical shift up 2 units, vertex \((0,2)\). - \(…
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divide: \\(210\\overline{)84,961}\\) \\(r\\) \\(\\square\\)
The quotient is \( 404\) and the remainder is \( 121\). So the first box (quotient) is \( 404\) and the second box (remainder) is \( 121\).
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10) $y = 3(x - 2)^2 - 3$ no calculators then describe the transformat $…
Vertex: \((2, -3)\), Axis of Symmetry: \( x = 2 \)
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divide: ( \begin{array}{r} square \\ 303 enclose{longdiv}{834,159} end{…
The quotient is \(2753\) and the remainder is \(0\), so the first box is \(2753\) and the second box (remainder) is \(0\).
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The vertical asymptote is \(x = -4\)
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put these numbers in order from least to greatest. \\(\\frac{339}{4}\\)…
\(83\frac{1}{2}\), \(84.01\), \(84.34\), \(\frac{339}{4}\)
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The function \(f(x)=\frac{3x^{2}+22x + 35}{3x + 15}\) has no vertical asymptotes (it has a hole at \(x = - 5\)).
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10) $y = 3(x - 2)^2 - 3$ v:( , ) a.s:
Vertex \( V:(2, - 3) \), Axis of Symmetry \( AS: x = 2 \)
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problems 1-4: determine the value of each expression. 1. $5 + (-3)$ 2. …
\( 2 \) ### Problem 2: \( -5 + 3 \)
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on a piece of paper, graph $y + 2 > -3x - 3$. then determine which answ…
The correct answer is the graph with a dashed line \(y = - 3x-5\) and shading above the line (including the point \((0,0)\)). If we assume the options are as described, and after …
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text description for graph a. (3, -1) b. (1, 5) c. (5, -5) d. (-3, -3)
B. \((1,5)\)
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graphing quadratics wkst date__________ period____ identify the vertex …
To solve these problems, we use the vertex form of a quadratic function \( y = a(x - h)^2 + k \), where the vertex is \( (h, k) \) and the axis of symmetry is \( x = h \). Let's c…
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question 7 of 10 what is the slope of the line described by the equatio…
C. -2
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3.3.3 quiz: point - slope equation of a line find a point - slope equat…
A. $y - 9 = 2(x - 1)$
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on a piece of paper, graph $y = -3x - 2$. then determine which answer m…
To determine the correct graph of \(y=-3x - 2\): 1. **Y - intercept**: When \(x = 0\), \(y=-3(0)-2=-2\), so the line passes through \((0,-2)\). 2. **Slope**: The slope \(m=-3\) (a…
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use the corresponding graphs to answer the following questions: 1. solv…
### Problem 1: Solve \( f(x) = 3 \) and \( f(x) = 7 \) using the graph of \( f(x) \) #### For \( f(x) = 3 \): # Explanation: ## Step 1: Analyze the graph of \( f(x) \) We look for…
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question 3 of 10 if ( f(x) = 5x - 12 ), what is ( f(2) )? a. ( -2 ) b. …
A. -2
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which of the following best describes the slope of the line below? a. z…
B. Undefined
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9. given that the general equation of a quadratic in factored form is (…
$f(x)=\frac{1}{2}(x-2)^2$
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a. -4 b. 4 c. $-\frac{1}{4}$ d. $\frac{1}{4}$
A. -4
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question 4 of 10 what is the slope of the line that contains the points…
C. -1
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what is the slope of the line shown below? (-7, 2) (4, 6) a. \\(\frac{1…
B. \(\frac{4}{11}\)
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what is happening to this graph when the x-values are between 4 and 8? …
C. It is constant.
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identify the range of the function shown in the graph. a. $0 < y < 3$ b…
C. \(y\geq0\)
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identify the domain of the function shown in the graph. a. $0leq xleq 8…
A. \( 0\leq x\leq8 \)
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is the graph increasing, decreasing, or constant? a. decreasing b. cons…
C. Increasing
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2.3.3 quiz: graphs of functions a. $-7 \\leq y \\leq 7$ b. $y = 1.5$ c.…
D. \( x \) is all real numbers.
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identify the vertical asymptotes of each. 9) $f(x)=\frac{x + 3}{x^{2}+2…
9) Vertical asymptote: $x=1$ 10) Vertical asymptotes: $x=2$ and $x=-2$
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other than a no solution set, use interval notation to express the solu…
The solution set in interval notation is \( (3, \infty) \). The correct graph is B.
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find the value of the expression $7 \\frac{1}{3} \\times y$ for $y = 1 …
$\frac{33}{4}$ (or $8\frac{1}{4}$)
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multiple transformations of linear functions choose a transformation to…
The transforming function \( f(x)=\boxed{x} \) (and the vertical translation is by 5 units, but the question about the transforming function is \( f(x)\), so the answer is \( x \)…
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graph the function $f(x) = -5^x$ on the axes below. you must plot the a…
The horizontal asymptote is \( y = 0 \). Two points with integer coordinates are \( (0,-1) \) and \( (1,-5) \) (or other valid integer - coordinate points like \( (2,-25) \), \( (…
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graph the function $f(x) = -5^x$ on the axes below. you must plot the a…
Asymptote: \( y = 0 \) Two points: \( (0, - 1) \) and \( (1, - 5) \) (you can plot these points and the asymptote \( y = 0 \) on the graph)
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10. find \\(\\frac{2}{3}\\) of 27.
18
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graph the function $f(x) = -5^x$ on the axes below. you must plot the a…
Asymptote: Horizontal (the equation of the asymptote is \( y = 0 \)). Two points: \( (0, - 1) \) and \( (1, - 5) \) (or other valid integer - coordinate points like \( (0, - 1) \)…
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mountain resort is about to launch a new and improved program. the prog…
The image provided is blurry and the text is not fully legible, making it impossible to accurately understand the question and the options. Please provide a clearer version or tra…
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graph the function $f(x) = -5^x - 4$ on the axes below. you must plot t…
The asymptote is horizontal with equation \( y=-4 \). Two points with integer coordinates are \( (0, -5) \) and \( (1, -9) \) (the asymptote is horizontal, \( y = - 4 \)).
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solve $21\\frac{3}{5} + 17\\frac{1}{4}$
$38\frac{17}{20}$ or $\frac{777}{20}$
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a) $f(x) = 3^x$ | $x$ | $f(x)$ | |-----|--------| | | | | | | | | | | |…
### Table of Values: | $x$ | $f(x)$ | |-----|--------| | $-2$ | $\frac{1}{9}\approx0.11$ | | $-1$ | $\frac{1}{3}\approx0.33$ | | $0$ | $1$ | | $1$ | $3$ | | $2$ | $9$ | ### Key Va…
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click and drag on elements in order order the steps for dividing decima…
1. Move the decimal in the divisor to the right until it is a whole number. 2. Move the decimal in the dividend equal number of places as in the divisor. 3. Place the decimal poin…
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create the transformed function g(x) from the basic linear function f(x…
The transformed function \( g(x) \) is \( \boldsymbol{g(x)=-2x + 5} \)
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that even if the company had been aware of waynes difficulty with his s…
9. All the above acts are negligence per se 10. A plaintiff must show that the defendant's act was both the factual cause of her injury as well as a foreseeable injury. 11. strict…
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question 3 given the function $f(x) = \\sqrt{x + 2}$: a. evaluate $f(2)…
a. $2$ b. $23$
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find the domain and range of the function: domain: range: (the table ha…
Domain: \( (-\infty, \infty) \) (or all real numbers) Range: \( (0, \infty) \) (or all positive real numbers)
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find the slope of the line graphed below.
\(-\frac{3}{2}\)
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compare f(x) = -0.3x² - 0.6x + 0.6 to function g, shown in the graph. w…
The maximum value of f is 0.9, and the maximum value of g is 4, so g has the greater maximum value.
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use a quadratic function to model the area of the rectangle. graph the …
The quadratic function is $A(x)=2x^2+14x+24$, and its graph is a parabola opening upwards with vertex at $(-3.5, -0.5)$, x-intercepts at $x=-3$ and $x=-4$, and y-intercept at $(0,…
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according to the u.s. constitution, the national government must guaran…
1. has a republican structure. 2. sheriff
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the function ( f ) is defined by ( f(x) = 2^x ) and the function ( g ) …
- When \( x = 4 \): \( f(4) = 16 \), \( g(4) = 32 \) - When \( x = 5 \): \( f(5) = 32 \), \( g(5) = 41 \) - When \( x = 6 \): \( f(6) = 64 \), \( g(6) = 52 \) ### Part 2:
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given the function below, fill in the table of values, use the table of…
- Table filled as above. - Domain: \(\boldsymbol{(-\infty,\infty)}\) (or all real numbers) - Range: \(\boldsymbol{(0,\infty)}\) (or all positive real numbers)
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for the following exercise, evaluate the function ( f ) at the indicate…
$f(3)=10$ $f(-2)=0$ $f(-a)=-2a+4$ $-f(a)=-2a-4$ $f(a+h)=2a+2h+4$
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systems by graphing e/m solve each system by graphing. 1). $y = \\frac{…
The solution (intersection point) is $(-2, 3)$ To graph: 1. For $y=\frac{1}{2}x + 4$: plot y-intercept $(0,4)$, then use slope $\frac{1}{2}$ (up 1, right 2) to plot a second point…
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use a quadratic function to model the area of the rectangle. graph the …
The quadratic function is $A(x)=2x^2+8x+6$, and its graph is a parabola opening upwards with vertex at $(-2, -2)$, x-intercepts at $x=-3$ and $x=-1$, and y-intercept at $(0,6)$.
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write the function in standard form. f(x) = 0.3(x - 3)^2 - 0.7 f(x) = (…
$f(x)=0.3x^2 - 1.8x + 2$
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find the compositions. $f(x) = 3x + 2, g(x) = x^2 - 4$ (a) $(f \\circ g…
\(3x^{2}-10\) ### Part (b)
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7. an exponential function is graphed on the grid. which function is be…
D. \( f(x)=3(\frac{7}{3})^x \) ### Question 8
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write a quadratic function to model the vertical motion for each situat…
The function is $\boldsymbol{h(t) = -16t^2 + 376t}$, and the maximum height is $\boldsymbol{2209}$ feet.
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if f(x) = 2x - 3, find the following: a. f(-2)
$-7$