微積分
極限、導數、最優化與函數性質。
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i can break apart 4/5 into \\(\\frac{3}{5} + \\frac{1}{5}\\) to help me…
$7\frac{1}{5}$
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how much money will each of the 4 siblings get to spend? $\\boxed{}$ an…
Each of the 4 siblings will get to spend \$3.75.
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question 2 of 10 which of the following functions best describes this g…
A. \(y = x^{2}-9x + 18\)
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graph the function $f(x) = 3(x - 6)^2$. plot the vertex. then plot anot…
The vertex is at \((6, 0)\). Another point on the parabola is \((7, 3)\) (or \((5, 3)\), etc.). To graph, plot \((6, 0)\) and then a point like \((7, 3)\) and draw the upward - op…
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1. fill in the blanks using your knowledge of place value units and bas…
a. 46 tens; 460 b. 46 hundreds; 4600 c. ones; 164 d. ten-thousands; 164000 e. 331 tens × 3 hundreds = 993 ten-thousands; 993000 f. 5 hundreds × 6 hundreds = 30 ten-thousands; 3000…
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write the equation of this line in slope - intercept form. write your a…
\( y = -\frac{1}{2}x + 50 \)
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name date 1. fill in the blanks using your knowledge of place value uni…
46; 460 ### Problem 1b
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select the simple subject. i limit my time watching television each day.
I
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has a slope of and a y-intercept (b) of options: 1, -1, 0, \\(\\frac{4}…
Slope: \(1\), y - intercept: \(1\)
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look at the graphs and their equations below. then fill in the informat…
(a) A: Positive B: Positive C: Negative D: Negative (b) B. B (c) C. C
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name write the correct answer for each sentence. $6\\frac{1}{2} + 4\\fr…
\( 11\frac{1}{6} \) ### 2. \( 3\frac{1}{6}+2\frac{3}{5} \)
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y = \\frac{1}{3}x - 10
30 If the question is "Find the y - intercept of the line \( y=\frac{1}{3}x - 10 \)":
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order these numbers from least to greatest. 7.88, 59/8, 7.364, 7 4/11
$7\frac{4}{11} < 7.364 < \frac{59}{8} < 7.88$
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graph this line using the slope and y-intercept: y = 8x + 1 click to se…
# Explanation: ## Step1: Identify y-intercept The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=8x + 1\), \(b = 1\). So the line …
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which equation matches the graph? options: y= -3x - 5 y= 3x + 5 y= 3x +…
D. $y=3x - 5$
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1. examine this table. a. which of these items would be hard for you to…
a. Gasoline would be hard to ration. It limits daily mobility for work, errands, and emergencies, and the tiered allotment system can create inequity and frustration, as it direct…
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graph the parabola. $y = 2x^2$ plot five points on the parabola: the ve…
Plot the points: $(0,0)$, $(-1,2)$, $(-2,8)$, $(1,2)$, $(2,8)$, then draw a smooth parabola through them.
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determine the domain on which the following function is increasing.
$x > 4$ or in interval notation: $(4, \infty)$
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graph the parabola $y = -3x^2$ plot five points on the parabola: the ve…
Five points to plot: 1. Vertex: $(0, 0)$ 2. Left points: $(-1, -3)$, $(-2, -12)$ 3. Right points: $(1, -3)$, $(2, -12)$ After plotting these points, click the "Graph-a-function" b…
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determine the domain on which the following function is decreasing.
The function is decreasing on the interval $(4, 13)$ or $4 < x < 13$
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write the equation of the line in fully simplified slope - intercept fo…
\(y = -x + 8\)
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2. 40\\overline{)3000}
750
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write the equation of the line in fully simplified slope - intercept fo…
\(y = -x + 12\)
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question write the equation of the line in fully simplified slope - int…
\(y=-x + 6\)
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leveled practice in 6 and 7, find each product. 6. $42.3 \\times 1 = \\…
6. $42.3$, $423$, $4230$ 7. $0.86$, $8.6$, $86$
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graph the following features: - y-intercept = -6 - slope = -1/2
The graph is a straight line with y - intercept at \((0, - 6)\) and slope \(-\frac{1}{2}\), passing through points like \((2,-7)\) and \((-2,-5)\) (or other points determined by t…
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solve the following system of inequalities graphically on the set of ax…
A point in the solution set is \( (0, 8) \) (or other valid points like \( (5, 4) \), \( (10, 8) \), etc.). The graphical solution is the region above both lines \( y = -\frac{4}{…
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write the equation of this line in slope - intercept form. write your a…
\(y=\frac{3}{2}x - 6\)
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9 multiple choice 1 point excludable goods... can be used by anyone can…
D. Can only be used by specific people
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at what value of x does the function given by $y = 3x^2 - 30x - 13$ tak…
\( 5 \)
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part 1 of 10 from the graph of the function, state the domain, the rang…
$(-\infty, \infty)$
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graph the following features: • y-intercept = -3 • slope = -2/5
The graph is a straight line passing through the point \((0, - 3)\) and other points such as \((5, - 5)\) (or \((-5, - 1)\)) with a slope of \(-\frac{2}{5}\). To visualize, plot \…
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use technology to find points and then graph the function $y = |x - 1| …
The five points to plot are $(-3,-1)$, $(-1,-3)$, $(1,-5)$, $(3,-3)$, $(5,-1)$. When connected, they form a V-shaped graph with vertex at $(1,-5)$.
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select all the solutions to the system of equations. (-4, 0) (-2, 8) (-…
\((-4, 0)\), \((0, 8)\)
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simplify. $2\\sqrt{3} \\cdot 3\\sqrt{15}$
\(18\sqrt{5}\)
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simplify $5sqrt3{81} + sqrt3{375}$.
\( 20\sqrt[3]{3} \)
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solve the following system of equations graphically on the set of axes …
La solución del sistema es \( (5, -3) \) (el punto de intersección de las dos líneas).
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172.6 ÷ 39
$\approx 4.43$ (rounded to two decimal places) or $\frac{863}{195}$ (exact fraction)
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6. the flight path of a firework is modeled by the relation $h(t) = -5(…
The maximum height reached by the firework is \( 100 \) meters, and it is reached at \( t = 4 \) seconds. ### Part (b)
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2. which number is not a common denominator of the fractions being adde…
D. 24
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the functions $f(x)$, $g(x)$, and $h(x)$ are shown below. select the op…
First, calculate average rates of change on $1 \leq x \leq 3$: 1. For $f(x)$: from graph, $f(1)=-30$, $f(3)=20$. Average rate: $\frac{20 - (-30)}{3-1}=25$ 2. For $g(x)$: $g(1)=6$,…
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which of the following are examples of limited resources on the part of…
C. time and money
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what is the slope of this line? simplify your answer and write it as a …
2
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find the value of $f(-6)$. $y = f(x)$ answer attempt 2 out of 2 submit …
7
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graph the system on a separate sheet of paper and determine the number …
D) 1 solution; \((-1, -2)\)
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what is the function rule for the linear function in this graph? slope–…
\( y=\frac{2}{3}x + 2 \) (The numerator of the slope is 2, the denominator is 3, and the y - intercept is 2)
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what is the function rule for the linear function in this table? slope–…
\( y = 6x+4 \)
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what is the function rule for the linear function in this table? slope-…
The function rule is \( y=-x + 6 \)
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graph the solution to the following system of inequalities. $y < -3x + …
The solution is the region that is below the dashed line \( y=-3x + 4 \) and above the solid line \( y = 3x - 2 \), with the intersection point of the two lines at \( (1,1) \). Th…
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graph the solution to the following system of inequalities. $y\\leq -3x…
1. Draw a solid line through $(0,4)$ and $(\frac{4}{3},0)$, shade below it. 2. Draw a dashed line through $(0,-3)$ and $(\frac{3}{2},0)$, shade above it. 3. The overlapping shaded…
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sketch the graph of the quadratic function $h(x) = 3x^2 - 12x + 9$ on t…
- Direction of opening: Upward - Axis of symmetry: \( x = 2 \) - Vertex: \( (2,-3) \) - x - intercepts: \( (1,0) \), \( (3,0) \) - y - intercept: \( (0,9) \) - Other points: \( (4…
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write the equation of the line in fully simplified slope-intercept form…
\(y = \frac{4}{3}x - 3\)
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solve the system of equations graphed on the coordinate axes below. $y …
The solution to the system is \( x = -1 \), \( y = 1 \) or the ordered pair \( (-1, 1) \)
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3.64)28.5376
\(7.84\)
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both of these functions grow as x gets larger and larger. which functio…
The function $f(x)=3(2)^x$ eventually exceeds $g(x)=7x + 3$.
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trevor sketched two graphs. first, he graphed this equation: \\( y = 5^…
\(y = - 5^{x}\)
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evaluate the function for the given value. $f(x) = \\begin{cases} 5x - …
$-21$
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write an exponential function for the graph. write the function in the …
$y=4(2)^x$
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which statement explains a long - term impact of the silk road on globa…
B. It created the first global trade network
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which statement best describes the silk road at its beginning? a religi…
D. A network of overland trade routes
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the following piecewise function: $f(x) = \\begin{cases} 3x + 1, & x \\…
To graph the piecewise function: 1. For \( y = 3x + 1 \) (\( x \leq 0 \)): Plot points like (0,1), (-1,-2), etc., and draw a line with slope 3 through these points, including the …
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select the correct answer. what is the main difference between third - …
B. An outside narrator relays the inner thoughts of one character in third-person limited point of view but those of more than one character in third-person omniscient point of vi…
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linear relationships write rules for linear functions with graphs that …
s: - For part a: The equation is \(y=\frac{2}{3}x - 1\) - For part b: The equation is \(y=-2x + 3\) - For the equation \(y =-\frac{1}{2}x-5\), \(m =-\frac{1}{2}\) and \(b=-5\)
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what is the slope of this line? options: $\frac{3}{4}$, $\frac{4}{3}$, …
\(\frac{3}{4}\) (corresponding to the option \(\frac{3}{4}\))
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in the context of behavioral economics, which of the following best des…
The item has sentimental value because it belongs to them. ### Question 16 (Describing Endowment Effect)
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14.26 × 5 ———
71.3
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what is the slope of this line? simplify your answer and write it as a …
$\frac{3}{5}$
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multiply. write your answer as a fraction in simplest form. \\(\\frac{3…
\(\frac{21}{10}\)
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3.76 × 4 ———
15.04
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2. $g(x) = |x - 4| + 2$ 4. $g(x) = |x + 7| - 1$ 6. $g(x) = |x + 5| - 3$
1. For $g(x)=|x-4|+2$: - Plot vertex $(4,2)$, then points $(0,6)$, $(-4,10)$, $(8,6)$, $(6,4)$; connect to form a V-shape opening upward. 2. For $g(x)=|x+7|-1$: - Plot vertex $(-7…
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6. write an equation, in point - slope form, for the line that is perpe…
The equation of the line in point - slope form is \(y - 2=-2(x - 6)\)
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8\\frac{5}{6} + 2\\frac{2}{3}
$11\frac{1}{2}$ (or $\frac{23}{2}$)
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question expand the logarithm fully using the properties of logs. expre…
$\log 9 + 3\log x$
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5\\frac{3}{4} - 2\\frac{1}{2}
$3\frac{1}{4}$ (or $\frac{13}{4}$)
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tony bought three books at a bookstore. here are their prices (in dolla…
The total amount Tony paid at the bookstore is $\$45.37$.
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graph each absolute value function. 1. $g(x) = |x + 1| + 1$ 3. $g(x) = …
1. For $g(x)=|x+1|+1$: - Vertex at $(-1, 1)$, additional points $(0, 2)$ and $(-2, 2)$; graph is a V-shape opening upward with these points. 3. For $g(x)=|x-3|-5$: - Vertex at $(3…
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which one doesn’t belong? which expression does not belong with the oth…
\( \frac{20}{8} \) does not belong with the other three because \( 2\frac{5}{8}=\frac{21}{8} \), \( \frac{8}{8}+\frac{8}{8}+\frac{5}{8}=\frac{21}{8} \), \( \frac{16}{8}+\frac{5}{8…
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2) on the set of axes below, graph $f(x) = |x - 3| + 2$. state the doma…
## Completed Table: | $x$ | $f(x)$ | |-----|--------| | 1 | 4 | | 2 | 3 | | 3 | 2 | | 4 | 3 | | 5 | 4 | ## Domain: All real numbers (or $(-\infty, \infty)$)
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1) on the set of axes below, graph the function $y = |x + 1|$ state the…
| $x$ | $y$ | |-----|-----| | $-3$| $2$ | | $-2$| $1$ | | $-1$| $0$ | | $0$ | $1$ | | $1$ | $2$ | | $2$ | $3$ | *(Note: The provided range $y\geq0$ and increasing domain $x>-1$ ar…
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which input value produces the same output value for the two functions …
\( x = 3 \) (the option with text "x = 3")
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5.82 × 8 ------
$46.56$
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Question was provided via image upload.
2 2 3 6
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graph the line with the equation $y = \\frac{1}{2}x + 5$.
The line passes through the y-intercept $(0, 5)$ and has a slope of $\frac{1}{2}$, so it can be graphed by plotting $(0,5)$ and a second point (e.g., $(2,6)$) then drawing a strai…
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graph the line with the equation $y = -\frac{1}{2}x - 4$.
The line passes through points such as $(0, -4)$ and $(2, -5)$, extending infinitely in both directions on the coordinate plane.
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function table complete the function table. plot the points and graph t…
### 4) $f(x)=x+4$ | $x$ | -20 | -16 | -8 | 0 | 4 | |-----|-----|-----|----|---|---| | $f(x)$ | -16 | -12 | -4 | 4 | 8 | *(Plot points $(-20,-16), (-16,-12), (-8,-4), (0,4), (4,8)$…
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which of these statements is best supported by the following passage (p…
D. Christopher is impressed at the variety and quantity of food Tracy is consuming at the business lunch.
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select the correct answer. what feature of a confederal system did the …
C. a limited central government linking independent states
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select the correct answer. imagine that an exchange student from china …
C. A limited government protects individual freedoms.
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which set of transformations can be used to obtain the graph of $g(x) =…
B. a vertical stretch by a factor of 2, followed by a shift of 3 units left
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the table shows several points that lie along a line when plotted on a …
\(y = 3x+1\)
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29. how would the equation $f(x) = \\log(x - 2) + 8$ be shifted with re…
right 2 units and up 8 units
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26. identify the ( x- ) and ( y- ) intercepts of the graph of ( f(x) = …
x-intercept: $(9, 0)$; found by setting $f(x)=0$ and solving for $x$ (since the numerator must be 0 for the rational function to equal 0, while the denominator is non-zero at $x=9…
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what impact did the magna carta have on the english monarchy? ○ it did …
It limited it.
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look at the list: - representative government - limited powers of gover…
democratic countries.
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how did the magna carta create the foundations of democratic rule in en…
The Magna Carta laid foundational democratic principles for England and the US by enshrining the rule of law, limiting executive power, and establishing precedents for individual …
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y = 2√x - 5; what are the transformations for the graph of the parent f…
A. Vertical Stretch by a factor of 2; translated down 5 units
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f(x) = \\sqrt3{x - 4} + 1; describe the transformation; options: right …
A. Right 4 units, up 1 unit
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f(x) = -\\frac{1}{3}\\sqrt{x + 1} - 5 given the function, which of the …
reflection over the x - axis, vertical compression by 1/3, horizontal shift left 1 and vertical shift down 5 (the fourth option)
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what kind of function is represented by the graph? options: cubic funct…
C. Cube Root Function
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which is the graph of the square root parent function?
B