微積分
極限、導數、最優化與函數性質。
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(1) $y=x^{2}+6x+7$ $=(x+3)^{2}-2$ $=(-3,-2)$ fill in the following tabl…
| $x$ | $y$ | |-----|-----| | $-6$ | $7$ | | $-5$ | $2$ | | $-4$ | $-1$ | | $-3$ | $-2$ | | $-2$ | $-1$ | | $-1$ | $2$ | | $0$ | $7$ |
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$f(x)=sin(x-h)+k$ what does the k do? shifts the graph up or down. up i…
A. Shifts the graph up or down. Up if positive and down if negative.
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$f(x) = pm a|x - h| - k$ what effect does \h\ have on the graph? 1. the…
Shifts the graph left or right. Right if positive and left if negative.
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what is the vertex of the following function? $y=4|x|+1$ $(-4,1)$ $(4,1…
(0,1)
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what is the vertex of the following function? $y=4|x|+1$ $(-4,1)$ $(4,1…
(0,1)
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step 2 canceling h from the numerator and denominator and evaluating th…
$\frac{1}{2}$
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use the given graph to estimate the value of each derivative. $y=f(x)$ …
(a) $f'(-3) = -1$ (b) $f'(-2) = 0$ (c) $f'(-1) = -1$ (d) $f'(0) = 1$ (e) $f'(1) = 0$ (f) $f'(2) = 0$ (g) $f'(3) = -2$
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what is the correct equation for this graph? $y \\leq |x-4| -1$ $y \\le…
A. $y \leq |x-4| -1$
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$f(x) = pm a |x - h| - k$ what does the \-\ in front of \a\ do to the g…
reflects the graph across the x-axis
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16. graph $f(x) = \\frac{1}{x}$ and compare it to $g(x)$ that is shown.…
1. A horizontal shift right 1 unit, a vertical shift up 2 units. 2. Let $C_A = 25h + 75$ and $C_B = 15h + 125$, where $C$ is total cost and $h$ is hours. 3. 5 hours
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which function is graphed? $f(x) = |x - 5| + 5$ $f(x) = |x| + 5$ $f(x) …
C. $f(x) = |x - 5|$
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below is the graph of $y=3^{x}$. translate it to become the graph of $y…
Translate the entire graph of $y=3^x$ **2 units to the right** and **1 unit upward**. The new graph will have a horizontal asymptote at $y=1$, pass through $(2,2)$ and $(3,4)$, an…
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score on last try: 0.63 of 1 pt. see details for more. at least one sco…
a) Yes it is continuous b) No rules are violated, the function is continuous.
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what is the correct equation for this graph? $y \\leq |x-4| -1$ $y \\le…
A. $y \leq |x-4| -1$
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announcements modules assignments grades 3c media lpc tutoring/raw libr…
$m = -7$ $c = 2$
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question 8 score on last try: 0 of 1 pt. see details for more. get a si…
$66$
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score on last try: 0 of 1 pt. see details for more. get a similar quest…
- $f(-6)$ is defined. - $\lim_{x \to -6} f(x)$ exists. - The function is not continuous at $x=-6$.
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current skill $ divide: $3\\frac{3}{4} \\div 3\\frac{1}{2}$ provide an …
$\frac{15}{14}$ or $1\frac{1}{14}$
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current skill $ divide: $3\\frac{3}{4} \\div 3\\frac{1}{2}$ provide an …
$\frac{15}{14}$ or $1\frac{1}{14}$
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order these numbers from least to greatest. $9.\\overline{5}$, $9\\frac…
$-\sqrt{100} < 9\frac{4}{11} < 9.46 < 9.\overline{5}$
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write the absolute value functions for the graph be14. let b = 115. let…
$y = \frac{4}{5}|x - 1| - 2$
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write the absolute value functions for the graphs below 14. let b = 1 1…
$y = |x - 1| - 2$ Vertex: $(1, -2)$ Point used: $(-1, 0)$ $h=1$, $k=-2$, $x=-1$, $y=0$
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exponential decay functions analyzing exponential decay graphs analyze …
The initial value is 2 The base, or rate of change, is $\frac{1}{2}$ The asymptote is $y=0$
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venth grade > ★ b.12 add and subtract integers subtract: $7 - -9 = \\sq…
16
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seventh grade > ★ b.12 add and subtract integers fns add: $1 + -7 = \\s…
$-6$
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seventh grade > ★ b.12 add and subtract integers add: $-6 + 9 = \\squar…
3
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eleventh grade > ★ b.12 add and subtract integers fns subtract: $1 - 4 …
$-3$
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seventh grade > ★ b.12 add and subtract integers fnadd:6 + -7 = □submit
$-1$
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seventh grade > ★ b.12 add and subtract integers fn add: $-3 + -8 = \\s…
$-11$
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seventh grade > ★ b.12 add and subtract integers add: $-6 + 9 = \\squar…
3
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my ixl seventh grade > ★ b.12 add and subtract integers fns subtract: $…
50
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seventh grade > ★ b.12 add and subtract integers fns add: $1 + -7 = \\s…
$-6$
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seventh grade > ★ b.12 add and subtract integers subtract: $7 - (-4) = …
11
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nth grade > ★ b.12 add and subtract integers add: $-2 + 2 = \\square$ s…
0
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seventh grade > ★ b.12 add and subtract integers subtract: $7 - (-4) = …
11
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venth grade > ★ b.12 add and subtract integers fns add: $5 + 10 = \\squ…
15
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seventh grade > ★ b.12 add and subtract integers fns add: $-5 + 5 = \\s…
0
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seventh grade > ★ b.12 add and subtract integers fns subtract: $-5 - 1 …
$-6$
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$y=mx+b$ 4) $y=-\frac{2}{3}x-1$ 5) $y=-x-1$ 6) $y=-2x-4$ 7) $y=-\frac{1…
### Graphs: 4. Line through $(0,-1)$ and $(3,-3)$ 5. Line through $(0,-1)$ and $(1,-2)$ 6. Line through $(0,-4)$ and $(1,-6)$ 7. Line through $(0,-1)$ and $(2,-2)$ 8. Vertical lin…
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
$m = 8$
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seventh grade > ★ b.12 add and subtract integers fns subtract: $-1 - -2…
1
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seventh grade > ★ b.12 add and subtract integers fns add: -4 + -1 = □ s…
$-5$
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multiple-choice question to find the average rate of change we will use…
slope $= \frac{16-0}{3-1}$
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question 5 of 14 step 1 of 2 consider the function: $h(x) = -4x^3 + 3x^…
43
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venth grade > ★ b.12 add and subtract integers fns add: $5 + 10 = \\squ…
15
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
(1, 0) (3, 16)
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describe how the graph of the function $y=(x-2)^2 - 1$ is related to th…
vertical translation: 1 unit down horizontal translation: 2 units right dilation: No dilation reflection: No reflection
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
y = 0 y = 16
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describe how the graph of the function $y=(x-2)^2 - 1$ is related to th…
vertical translation: 1 unit down horizontal translation: 2 units right dilation: No dilation reflection: No reflection
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describe how the graph of the function $y = -(x + 4)^2 - 6$ is related …
vertical translation: 6 units down horizontal translation: 4 units left dilation: No dilation (no stretch or compression) reflection: Reflected over the x-axis
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does the parabola $y=2x^{2}-17x+7$ have a tangent line whose slope is -…
A. The parabola has a tangent line whose slope is -1. The equation of the tangent line is $y = -x -25$ and the point of tangency is $(4, -29)$.
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
y = 0 y = 16
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describe how the graph of the function is related to the graph of the p…
It is reflected over the x-axis, vertically stretched by a factor of 4, and has no horizontal/vertical shift.
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question 9 1/1 pt the graph of $y=f(x)$ (solid) and $y=g(x)$ (dashed) i…
$-\infty$
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compute the right-hand and left-hand derivatives as limits and check wh…
Left-hand derivative at $P(9,6)$: $\frac{1}{6}$ Right-hand derivative at $P(9,6)$: $2$ The function is not differentiable at point $P$.
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$\\sqrt{128}$
$8\sqrt{2}$
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differentiate the function. then find an equation of the tangent line a…
The derivative is $-\frac{5}{2(x-2)^{\frac{3}{2}}}$ An equation of the tangent line is $y=-\frac{5}{2}x+\frac{25}{2}$ (or in standard form: $5x+2y=25$)
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9. a tangent function of the form $y = \\tan(bx)$ is defined for all va…
$\frac{1}{4}$ (any value $0<|b|\leq\frac{1}{4}$ is valid, $\frac{1}{4}$ is one example)
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
f(1) = 0
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1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
a = 1, b = 3
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check all that apply: $\frac{sin(2x)}{sin(9x)} =$$square sinleft(\frac{…
$\frac{2}{9}$
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vocab quiz 2 which statement best explains a key difference between saf…
Safety net programs provide direct assistance, while environmental policies set limits on actions to protect public goods
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vocab quiz 2 2 of 10 a government limits industrial emissions even thou…
The use of regulatory power to protect environmental and public health
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1) $y = \\frac{3}{4}x - 2$
The line $y=\frac{3}{4}x-2$ is graphed by plotting the y-intercept $(0, -2)$, using the slope to find a second point $(4, 1)$, and drawing a straight line through these two points.
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steps for graphing 1 start by placing a point at the y-ic_ 2 from that …
2
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y-intercept = $\boldsymbol{3}$ slope = $\boldsymbol{\frac{3}{2}}$ equat…
-3
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graph the following features: - slope = 2 - y-intercept = $-2$ answer a…
The line $y=2x-2$ is graphed by plotting $(0, -2)$ and $(1, 0)$, then drawing a straight line through these points and extending it.
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graphing sine, cosine and tangent ariel gaspar lopez 9 of 14 enter an e…
$f(x)=3.5\cos(x)$
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name: _______ period____ find the slope, y-intercept of the line, and t…
1. $m=-\frac{4}{3}$, $b=\frac{20}{3}$, Equation: $y=-\frac{4}{3}x+\frac{20}{3}$ 2. $m=-\frac{3}{4}$, $b=-\frac{19}{4}$, Equation: $y=-\frac{3}{4}x-\frac{19}{4}$ 3. $m=0$, $b=3$, E…
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which concept describes the idea that government and government officia…
rule of law
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$24div(3+5)\times2$
6
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the constitution regulates government powers byproviding guides and lim…
providing guides and limits to the government's power.
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solve each problem paying careful attention to the order of operations.…
1. $20 \div 5 + 2 = 6$ 2. $18 \div 9 \times 6 = 12$ 3. $2 \times 8 \div 4 = 4$ 4. $20 - 5 \times 4 = 0$ 5. $2 \times 6 + 4 \times 3 = 24$ 6. $20 \div 2 \times 3 - 6 = 24$ 7. $(2 +…
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8. $32 + 12 \\div 4$
12
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7. $(18 - 6) \\div 3 + 4$
8
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question ⓘ governments may choose to censor access to the internet in a…
Preventing access to video or photo sharing services
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3. twelve divided by the difference of 8 and 2
2
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solve each problem paying careful attention to the order of operations.…
1. $20 \div 5 + 2 = 6$ 2. $18 \div 9 \times 6 = 12$ 3. $2 \times 8 \div 4 = 4$ 4. $20 - 5 \times 4 = 0$ 5. $2 \times 6 + 4 \times 3 = 24$ 6. $20 \div 2 \times 3 - 6 = 24$ 7. $(2 +…
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2) $12 + 4^2$
28
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28) $f(x)=-x^2 - 4x + 1$; find $f(1)$
$-4$
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which best describes emersons central message to his contemporaries in …
One should follow one's conscience instead of what others dictate.
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1 multiple choice 1 point what do we know about the family structure of…
1. They partnered with a spouse of their choice, raised small nuclear families, and occasionally separated and remarried. 2. Socities adopted male-dominated, extended families wit…
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27) $f(x)=x^2 - 2x - 1$; find $f(2)$
$-1$
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key features of graphs 6. name: even degree or odd degree? end behavior…
Even Degree or Odd Degree? Even Degree End Behavior: As \(x\to\infty\), \(f(x)\to-\infty\); As \(x\to-\infty\), \(f(x)\to-\infty\) X-Intercepts: \((-6.861, 0)\), \((5.238, 0)\) Y-…
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$f(x)=3x + 5$; find $f(-3)$ 28) $f(x)=-x^2 - 4x + 1$;
$-4$ Note: The second function $f(x)=-x^2-4x+1$ is incomplete (the value to evaluate is missing), so only the solution for $f(x)=3x+5; \text{Find }f(-3)$ is provided. If you provi…
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25) $f(x) = -3x$; find $f(-3)$
9
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slt12: key features of graphs name: 4. even degree or odd degree? end b…
Even Degree or Odd Degree? Odd Degree End Behavior: As $x\to-\infty$, $f(x)\to-\infty$; as $x\to+\infty$, $f(x)\to+\infty$ X-Intercepts: $(-1.8541, 0)$, $(0, 0)$, $(4.8541, 0)$ Y-…
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evaluate each function for the given value. 24) $f(x) = -x^2 - 6x - 7$;…
$-2$
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brain breaker #5: what would you do about the petition if you were the …
1. Brain Breaker #5: I would first review the colonial petition's grievances thoroughly, then negotiate a compromise that reduces the tax burden on colonists while upholding limit…
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2. even degree or odd degree? end behavior: x-intercepts: y-intercept: …
Even Degree or Odd Degree? Odd Degree End Behavior: As $x\to+\infty$, $f(x)\to-\infty$; As $x\to-\infty$, $f(x)\to+\infty$ X-Intercepts: $(-2.84, 0)$, $(1, 0)$, $(2.52, 0)$ Y-Inte…
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• the correct answer is: problem 3 $(5 + 3)^2 - 4 \\times 2$ student wo…
The student failed to follow the order of operations (PEMDAS/BODMAS) by not calculating the sum inside the parentheses $(5+3)$ first. Instead, they incorrectly calculated $3^2$ be…
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solve each equation making sure to follow the order of operations. $2 \…
1. $2 \times 8 + 7$: 23 2. $2 + 3 \times 9$: 29 3. $4 + 10 \div 2$: 9 4. $9 - 2 + 3$: 10 5. $(3 + 2) \times 9$: 45 6. $8 \div (2 + 2)$: 2 7. $6 \div 2 - 1$: 2 8. $1 + 3 \times 5$:…
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8 mark for review the industrialization of japan in the nineteenth cent…
D. A policy of imperial expansion that sought to take advantage of the political and military weakness of neighboring Asian states
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the exponential function $g(x)=3^{x - 1}-4$ is a transformation of the …
B. $g(x)$ is translated 6 units down. E. $g(x)$ is translated 1 unit to the right.
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thursday 2/5 what went wrong? - order of operations directions: each pr…
What went wrong? The student added before doing the required division step after calculating the exponent, violating the order of operations. Correct solution: $\frac{28}{3}$ (or …
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question determine whether the following graph represents a function. a…
Not a Function
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1. which of the following is equivalent to $76\\div9$? a $\frac{9}{76}$…
1. B. $8\frac{4}{9}$ 2. A. 6 3. B. 72 inches 4. C. $10^3$
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which of the graphs shown has a constant rate of change? a. graph w onl…
D. Graph X only
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determine whether the function represents exponential growth or decay. …
The function $y = 500 \cdot 4^x$ represents exponential **growth**. Rewriting the base in terms of the rate of growth or decay results in the function $y = 500 \cdot \boldsymbol{(…
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1. which of the following is equivalent to $76\\div9$? a $\frac{9}{76}$…
1. B. $8\frac{4}{9}$ 2. A. 6 3. B. 72 inches 4. C. $10^3$