微積分
極限、導數、最優化與函數性質。
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swine flu is attacking porkopolis. the function below determines how ma…
\( 32 \) (since \( S \) is in thousands, it means 32 thousand people) ### Part (b)
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find the slope of the line ( y = -\frac{3}{2} ). write your answer as a…
\( 0 \)
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swine flu is attacking porkopolis. the function below determines how ma…
32 ### Part (b)
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use the graph of g(x), k(x) = 4x - 5, and h(x) = \\(\\frac{x}{10}\\) to…
a) \( \boldsymbol{1} \) b) \( \boldsymbol{5} \) c) \( \boldsymbol{-6} \) d) \( \boldsymbol{3} \) and \( \boldsymbol{6} \) (If we consider the graph, the \( x \)-values where \( g(…
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use the graph of g(x), k(x) = 4x - 5, and h(x) = \\frac{x}{10} to evalu…
s: a) \( \boxed{0} \) b) \( \boxed{5} \) c) \( \boxed{-6} \) d) \( \boxed{3} \) (or \( \boxed{6} \), but likely 3 or 6; need to check graph again. Wait, maybe I made a mistake in …
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if an item regularly costs d dollars and is discounted 12 percent, whic…
0.88d (the first option)
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if $y = 2x^2 - 4x - 5$ what is the value when $x = -3$ 20 25 15 30
25
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mr. willbury buys a bag of granola for snacks. the graph shows the tota…
\(y=-4x + 14\)
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what is one way a command economy affects the lives of private citizens…
A. Citizens cannot make most economic decisions.
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which of the following graphs could represent a cubic function? a. grap…
C. Graph C
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which of the following graphs could represent a quartic function? a. gr…
Graph C
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the graph of a logarithmic function is shown. select the function which…
C. \( y = \log_3(x + 2) \)
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todays review opportunity identify the initial value and rate of change…
Initial value \(=1\), rate of change \(=2\), equation \(y = 2x+1\)
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at what values of x, does f(x) = 0? check all that apply.
\( x = 1 \)
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which of the following graphs could represent a cubic function? graph d…
C. Graph C
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which of the following graphs could represent a quartic function? a. gr…
A. Graph A
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at what values of x, does f(x) = 0? check all that apply.
\(x=-1\) and \(x = 2\)
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at what values of x, does f(x) = 0? check all that apply. options: 1, -…
\(-4\), \(3\)
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evaluate the function below for x = 3. f(x) = x³ + 5x² + 1 options: 40,…
\(81\) ---
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question 1 of 20 the truman doctrine said that: a. america would provid…
C. America would fight to limit the spread of Communism.
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knowledge check 1 no time limit default module module 1 of 1 question 9…
D. In the metal transfer pan
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find the domain of the function. $h(x) = \\dfrac{11}{\\dfrac{6}{x} - 1}…
\( (-\infty, 0)\cup(0, 6)\cup(6, \infty) \)
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y = |x| - 1 column by column x |x| y = |x| - 1 -3 -2 -1 0 1 2 3 try
For \(x = -3\), \(|x| = 3\) and \(y = |x| - 1 = 2\).
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graph the equation y = |x| - 5. let x = -3, -2, -1, 0, 1, 2, and 3. fin…
(for y - values table): | x | y | |----|----| | - 3 | - 2 | | - 2 | - 3 | | - 1 | - 4 | | 0 | - 5 | | 1 | - 4 | | 2 | - 3 | | 3 | - 2 |
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evaluate the piecewise function at the given values of the independent …
(a) \( f(-3) = \boldsymbol{-4} \) (b) \( f(0) = \boldsymbol{7} \) (c) \( f(2) = \boldsymbol{13} \)
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write the point - slope form of the lines equation satisfying the given…
- Point - slope form: \( y - 3=0(x + 6) \) (or \( y - 3=0(x - 0) \)) - Slope - intercept form: \( y = 3 \)
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15. graph: function in standard form: ( q(x) = x^3 + 2x^2 + x + 2 ) fun…
- End behavior: As \( x ightarrow\infty \), \( q(x) ightarrow\infty \); As \( x ightarrow-\infty \), \( q(x) ightarrow-\infty \) (if leading coefficient is 1) or As \( x ightarrow…
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15. (two-step linear inequalities mc) solve the inequality and graph th…
The third graph (the one with an open circle at -8 and an arrow pointing to the left, starting from -14 to -5 with the open circle at -8 and arrow left)
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what are the vertical asymptotes of y = cot x for -3π ≤ x ≤ 3π? only ±π…
B. \(0, \pm\pi, \pm2\pi, \pm3\pi\)
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which of the following represents $y = \\cot x$ ?
The graph on the Bottom-Right (the red graph)
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secondary math iii // module 3 polynomial functions - 3.10 11. function…
The standard form of \( g(x) \) is \( -x^3 + 6x^2-8x \)
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set topic: reviewing features of polynomials some information has been …
- **Function in factored form**: \( f(x)=x\cdot x\cdot x \) (or \( f(x)=x^3 \) as factored form with repeated factor) - **End behavior**: As \( x ightarrow -\infty \), \( f(x) igh…
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find the intercepts and graph the equation by plotting points. y = 2x +…
A. The intercept(s) is/are \((-2, 0)\) and \((0, 4)\) (for x and y intercepts respectively; if single intercept asked, but here two exist). To graph, plot these points and draw th…
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what is the true solution to $2 \\ln 4x = 2 \\ln 8$? $\\bigcirc$ $x = -…
\(x = 2\) (corresponding to the option "x = 2")
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the graph shows a function. is the function even, odd, or neither? use …
For the function on the graph, opposite \(x -\)values have opposite \(y -\)values. This shows the function is odd because its graph has symmetry about the origin.
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describe how the value of expression a compares to the value of express…
42 less than
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given the function ( f(x) = (x + 11)^3 ), complete parts a through c. (…
The correct graph is Option B.
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find the slope of the line passing through the points given below or st…
For the slope part: A. The slope is \( 3 \) For the direction part: D. The line rises from left to right
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the cost of publishing a poster is $3000 for setting up the printing eq…
6000
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begin by graphing f(x) = log x. use transformations of this graph to gr…
- **Asymptote Equation**: \( x = 0 \) - **Domain**: \( (0, \infty) \) - **Range**: \( (-\infty, \infty) \) (For graphing: Start with the graph of \( y = \log x \), then shift ever…
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find the zeros for the polynomial function and give the multiplicity fo…
The zero(s) is/are \(-7, - 4, 4\) For the multiplicities: We choose option C. The multiplicity of the smallest zero (\(-7\)) is \(1\). The multiplicity of the largest zero (\(4\))…
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use the graph to determine (a) open intervals on which the function is …
s: (a) A. The function is increasing on the interval(s) \( (2, 3), (4, 5) \). (b) A. The function is decreasing on the interval(s) \( (3, 4), (5, \infty) \). (c) B. The function i…
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evaluate or simplify the expression without using a calculator. $ln e^{…
$9x$
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use the graph of f to determine each of the following (a) the domain of…
(h) The relative maximum of the graph is where \(f(x)=\boxed{4}\) (i) \(f(x) = 3\) where \(x=\boxed{-4,-2}\) (Wait, no, maybe - 4 and 0? Wait, I think I messed up. Alternatively, …
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graph the given functions, f and g, in the same rectangular coordinate …
For \( f(x) \) table (x=4,9): f(4)=2, f(9)=3. For \( g(x) \) table (x=1,6): g(1)=2, g(6)=3. The graph of \( g(x) \) is the graph of \( f(x) \) shifted left by 3 units (since \( g(…
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begin by graphing f(x) = \\log_3 x. then use transformations of this gr…
Vertical Asymptote: \( x = -5 \) Domain: \( (-5, \infty) \) Range: \( (-\infty, \infty) \)
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find the horizontal asymptote, if any, of the graph of the rational fun…
B. There is no horizontal asymptote.
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use the graph of y = f(x) to graph the function g(x) = f(x + 1) + 6. ch…
A. The graph corresponding to Option A
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graph the line with the equation $y = -\frac{1}{2}x - 3$.
Plot the point \((0, - 3)\) (y - intercept). Then, using the slope \(m =-\frac{1}{2}\), from \((0,-3)\) move 2 units right and 1 unit down to get \((2,-4)\). Connect these two poi…
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evaluate the following expression without using a calculator.\\(\\log_{…
$\frac{1}{2}$
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use properties of logarithms to expand the logarithmic expression below…
$\frac{1}{2}\log_{d} x + 6\log_{d} y - 8\log_{d} z$
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find the domain of the logarithmic function. f(x) = log (3 - x) the dom…
\((-\infty, 3)\)
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for the polynomial function f(x) = (x - 4)²(x + 3)(x - 1), answer parts…
A. The graph of f(x) rises to the left and rises to the right.
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((10 - 6 + 5) ÷ 9) × 2
\(2\)
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for each problem, find the x and y intercepts, x-coordinates of the cri…
x - intercepts: \(x = 0, x = 3\); y - intercept: \(y = 0\); critical points: \(x = 0,x = 2\); increasing on \((0,2)\), decreasing on \((-\infty,0)\cup(2,\infty)\); inflection poin…
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find an nth-degree polynomial function with real coefficients satisfyin…
\(-2x^3 + 8x^2 - 8x + 32\)
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for each problem, find the: x and y intercepts, x - coordinates of the …
x - intercepts: \(x = 0\) and \(x = 3\); y - intercept: \(y = 0\); critical points: \(x = 0\) and \(x = 2\); increasing: \((0,2)\); decreasing: \((-\infty,0)\) and \((2,\infty)\);…
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evaluate $y = \\ln (x - 2)$ for the following values of $x$. round to t…
For \( x = 3 \), \( y = 0 \); for \( x = 4 \), \( y\approx0.693 \); for \( x = 6 \), \( y\approx1.386 \)
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evaluate the expression without using a calculator. \\log_{2}(\\log_{5}…
0
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$\\int_{0}^{8} \\frac{dx}{\\sqrt{1 + x}}$
4
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when the area in square units of an expanding circle is increasing twic…
\(\frac{1}{\pi}\)
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the function f is defined by an equation of the form $f(x) = a(b)^x + c…
A. \( f(x) = -3(5)^x - 4 \)
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find the indicated value of the logarithmic function. ln (e^5) ... the …
5
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find all the zeros of the polynomial function. use the rational zero th…
-2, 1, 4
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if f(x) = -2|x| + 8, what is f(-1.8)? ○ 4 ○ 6 ○ 10 ○ 12
4 (the first option, A. 4 if options are labeled A, B, C, D as 4,6,10,12)
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the graph represents f(x) = \\lceil x \ ceil + 3. what is f(-2.2)? \\bi…
0
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the step function f(x) is graphed. what is the value of f(-1)? -3 -1 0 1
-1 (the option is " - 1" or the option with - 1, which is the second option: " - 1")
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what is the domain of the step function $f(x) = \\lfloor 2x \ floor - 1…
\(\{x|x\text{ is a real number}\}\)
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the number line models the expression 476 - 289. enter numbers to label…
- The jump from 476 to 400: \( \boldsymbol{76} \) - The jump from 400 to the left: \( \boldsymbol{213} \) - The leftmost box (result): \( \boldsymbol{187} \) (Assuming the boxes a…
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which is the graph of the step function f(x)? $f(x)=\\begin{cases}-1, &…
The graph that matches is the first one (the upper graph among the two shown, with segments at \( y = -1 \) (left), \( y = 0 \) (middle), and \( y = 1 \) (right)).
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for f(x)=5x−1 and g(x)=5x²−1, find the following functions. a. (f∘g)(x)…
s: a. \((f \circ g)(x)=\boldsymbol{25x^{2}-6}\) b. \((g \circ f)(x)=\boldsymbol{125x^{2}-50x + 4}\) c. \((f \circ g)(2)=\boldsymbol{94}\) d. \((g \circ f)(2)=\boldsymbol{404}\)
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nina graphs the function $y=\\lfloor x \ floor$ to learn the properties…
A. 5
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1. simplify the expression: $(1^4 \\times 2^2 + 3^3) - 2^5 \\div 4$.\ a…
D) 23
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evaluate the function at the given values of the independent variable a…
(a) \(\frac{44}{9}\) (b) \(\frac{44}{9}\) (c) \(\frac{5x^{2}-1}{x^{2}}\)
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divide and express the result in standard form. \\(\\frac{9}{6 - i}\\) …
\(\frac{54}{37}+\frac{9}{37}i\)
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question use technology to find points and then graph the function $y =…
To graph \(y = \sqrt[3]{x}-1\), plot points such as \((-7,-2.913)\), \((0,-1)\), \((1,0)\), \((2,0.26)\), \((9,1.08)\) (and draw a smooth curve through them).
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question a rocket is launched in the air. its height in feet is given b…
The x - coordinate (or t - coordinate) of the vertex is \( 2 \) and represents the time (in seconds) when the rocket reaches its maximum height. The y - coordinate (or h - coordin…
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line equations from point/slope question what is the equation of the li…
\( x = 3 \)
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topic: subtracting whole numbers and applications progress: question id…
A. $1,504
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graph the parabola and give its vertex, axis of symmetry, x-intercepts,…
12
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line equations from point/slope question what is the equation of the li…
The equation of the line is $y=-5x + 6$ (or $5x + y=6$)
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topic: comparing whole numbers progress: the movement of the progress b…
C. \(31 > 13\) (assuming option labels, but based on the correct expression, the answer is the option with \(31 > 13\))
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question what is the equation of the line that passes through the point…
The equation of the line is $y=-\frac{5}{6}x + 5$ (or $5x + 6y=30$)
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write the equation of the line in fully simplified slope-intercept form…
\( y = \frac{3}{2}x - 5 \)
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write the equation of the line in fully simplified slope-intercept form.
\(y = 2x - 5\)
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prove: \\(\\log_a \\left(\\frac{x}{y}\ ight) = \\log_a x - \\log_a y\\)…
\( a^{m - n} \)
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prove: \\(\\log_a \\left(\\frac{x}{y}\ ight) = \\log_a x - \\log_a y\\)…
$x = \boldsymbol{a^{m}}$ and $y = \boldsymbol{a^{n}}$
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solve the equation. $e^{x - 1} = 9$ select the correct choice below and…
A. \( x = 3.1972 \)
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solve the equation. ln x + ln 3x = -1 select the correct choice and fil…
A. \(x = 0.3502\)
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solve the equation for r. \\(\\log_{r} 3 = \\frac{1}{3}\\) select the c…
A. $r = 27$
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use natural logarithms to evaluate the logarithm to the nearest thousan…
$5.644$
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in the given equation, q is an integer constant. the given equation has…
\(7\)
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use natural logarithms to evaluate the logarithm to the nearest thousan…
1.420
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use the properties of logarithms to write the expression as a sum, diff…
$\log_7 2 + \log_7 k$
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in 1971, the ny times published the pentagon papers which revealed that…
War Powers Act of 1973; Fall of Saigon
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in 1971, the ny times published the pentagon papers which revealed that…
: War Powers Act; Fall of Saigon # Brief Explanations: The first blank refers to the 1973 War Powers Act, which limits presidential authority to deploy troops without congressiona…
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evaluate the logarithm without using a calculator. \\(\\log_{2} \\frac{…
\(-4\)
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the shaded region shown represents the solutions to the inequality -16y…
D. 96
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the function f is defined by $f(x) = \\frac{7}{13}x$. what is the slope…
B. \(\frac{7}{13}\)
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13 mark for review an exponential function f is defined by f(x) = k(3)^…
D. 18