Calculus
Limits, derivatives, optimization, and behavior of functions.
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$f(x) = \\frac{3}{4}x - 3$ evaluate $f(-8)$ type answer here.
$-9$
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$f(x) = \\frac{3}{4}x - 3$ evaluate $f(-8)$ type answer here.
$-9$
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$f(x) = -3x - 4$ evaluate $f(-2)$
$2$
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if $f(x)$ is an exponential function of the form of $y = ab^{x}$ where …
$21.5$
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question if $f(x)$ is an exponential function of the form of $y = ab^{x…
21.2
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graph the following function. $y = 5 \\cdot 2^{x}$ show your work here …
- Horizontal asymptote: $y=0$ - Plotted points: $(-2, 1.25)$, $(-1, 2.5)$, $(0, 5)$, $(1, 10)$ - The graph is an increasing exponential curve that approaches the x-axis (from abov…
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multiple-choice question using the function below. $g(x)=2(6)^x$ calcul…
$m = 35$
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question write an exponential function in the form $y = ab^x$ that goes…
$y=13(2)^x$
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question write an exponential function in the form $y = ab^x$ that goes…
$y=13(2)^x$
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consider the definite integral $int_{0}^{1} xe^{4x^{2}+b}dx$, where $b$…
The substituted definite integral is $\boldsymbol{\int_{b}^{4+b} \frac{1}{8}e^u du}$
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consider the definite integral $int_{0}^{1} xe^{4x^{2}+b}dx$, where $b$…
The substituted definite integral is $\boldsymbol{\int_{b}^{4+b} \frac{1}{8}e^u du}$
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20. given the exponential function: $f(x) = 5 \\cdot 2^{x-2} + 1$, expl…
- The factor 5 vertically stretches the parent exponential function $2^x$ by a factor of 5. - The $-2$ in the exponent shifts the parent function 2 units to the right. - The $+1$ …
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graph this function:$f(x) = -2x - 16$graph this function:$f(x) = \\frac…
1. For $f(x) = -2x - 16$: - Y-intercept: $(0, -16)$ - X-intercept: $(-8, 0)$ - Draw a straight line through these two points, extending across the grid. 2. For $f(x) = \frac{1}{2}…
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homework 2: 1.5 substitution score: 18/35 answered: 6/9 question 7 cons…
a) $x^3 + 4$ b) $3x^2 dx$ c) Lower limit: $12$, Integrand: $\frac{1}{3u^{14}}$, Upper limit: $220$ Transformed integral: $\boldsymbol{\int_{12}^{220} \frac{1}{3u^{14}} du}$
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unit 4 dividing fractions: end of unit study guide for all questions: w…
1. 32 square inches 2. $\frac{3}{5}$ 3. $\frac{5}{7}$ 4. $3$ 5. $6$ 6. $2\frac{1}{12}$ o $\frac{25}{12}$ 7. $5\frac{1}{7}$ o $\frac{36}{7}$
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homework 2: 1.5 substitution score: 14/35 answered: 5/9 question 6 cons…
a) $u = x^7 + 7$ $du = 7x^6 dx$ c) $\frac{1}{7} u^{1/5} du$ (or $\frac{1}{7} \sqrt[5]{u} du$)
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homework 2: 1.5 substitution score: 10/35 answered: 4/9 question 5 cons…
a) $u = 1 + 9x^8$ $du = 72x^7 dx$ c) $\frac{1}{9} \int u^{-\frac{1}{2}} du$ d) $\frac{2}{9}\sqrt{1 + 9x^8}$
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homework 2: 1.5 substitution score: 6/35 answered: 3/9 progress saved q…
a) $u = \sin(x)$ $du = \cos(x) dx$ c) $\int u^{27} du$ d) $\frac{\sin^{28}(x)}{28}$
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score on last try: 3 of 4 pts. see details for more. at least one score…
$\boldsymbol{\int \frac{1}{5}u^{34} du}$ *(Note: The integral in part c) was marked incorrectly in the image; this is the correct substituted integral. The final antiderivative in…
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estimate the sum. $18\\frac{5}{8} + 18\\frac{10}{13} \\approx \\square$…
38
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estimate the sum. $14\\frac{4}{5} + 14\\frac{5}{17} \\approx \\square$ …
29
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homework 2: 1.5 substitution score: 6/35 answered: 3/9 progress saved q…
a) $u = \sin(x)$ $du = \cos(x) dx$ c) $\int u^{27} du$ d) $\frac{\sin^{28}(x)}{28}$
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consider the integral below.$int \frac{7}{9x + 3}dx$which integral corr…
$\boldsymbol{\int \frac{7}{9u} du}$
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lines 1-14 from the song \bohemian rhapsody\ by queen is this the real …
9. D. Guilt and fear 10. A. The narrator realizes their life has been permanently altered 11. B. Shows that the narrator has accepted the situation and the consequences of their a…
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score: 0/35 answered: 0/9 question 1 consider the integral below. $int …
$\boldsymbol{\int \frac{4u^{-8}}{7}du}$
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round to the nearest whole number. $9\\frac{1}{5} \\approx \\square$ ch…
9
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$\\frac{12}{14} \\times \\frac{1}{4} =$
$\frac{3}{14}$
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round to the nearest whole number. $9\\frac{1}{5} \\approx \\square$ ch…
9
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round to the nearest whole number. $18\\frac{10}{19} \\approx \\square$…
19
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$1.5 cdot 2^{1}$
3
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15. given the function below, fill in the table of values and use the t…
### Completed Table: | $x$ | $-2x$ | $y=-2x+1$ | |-----|-------|-----------| | $-3$ | $6$ | $7$ | | $-2$ | $4$ | $5$ | | $-1$ | $2$ | $3$ | | $0$ | $0$ | $1$ | | $1$ | $-2$ | $-1$…
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look at this graph: what is the y-intercept?
$-7$
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look at this graph: what is the y-intercept?
$-7$
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-1.6$ or $\boldsymbol{-\frac{8}{5}}$
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exponential functions name complete the table and then graph the expone…
Tabla completada: | $x$ | $y$ | |-----|-----| | -2 | $-\frac{1}{4}$ | | -1 | $-\frac{1}{2}$ | | 0 | $-1$ | | 1 | $-2$ | | 2 | $-4$ | | 3 | $-8$ | | 4 | $-16$ | Para graficar: Marc…
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given the function $g(x) = x^2 - 10x + 18$, determine the average rate …
$2$
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given the function $g(x) = x^2 - 10x + 18$, determine the average rate …
$2$
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14. given the function below, fill in the table of values and use the t…
### Completed Table: | $x$ | $4x$ | $y=4x-4$ | |-----|------|----------| | $-3$ | $-12$ | $-16$ | | $-2$ | $-8$ | $-12$ | | $-1$ | $-4$ | $-8$ | | $0$ | $0$ | $-4$ | | $1$ | $4$ |…
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match each graph below with the appropriate function. a) $f(x)=3+\\log_…
$\boldsymbol{f(x) = -5 + \log_2 x}$
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let $f(x)=x^2$ and $g(x)=\\sqrt{x}$. find $f \\circ g$ and $g \\circ f$…
a) $(f \circ g)(x) = x$ (for $x\geq0$) b) $(g \circ f)(x) = |x|$ (or $x$ for $x\geq0$) c) $(f \circ g)(3) = 3$ d) $(g \circ f)(3) = 3$
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let $f(x)=x^2$ and $g(x)=\\sqrt{x}$. find $f \\circ g$ and $g \\circ f$…
a) $(f \circ g)(x) = x$ (for $x\geq0$) b) $(g \circ f)(x) = |x|$ (or $x$ for $x\geq0$) c) $(f \circ g)(3) = 3$ d) $(g \circ f)(3) = 3$
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show all your workfor questions 1 – 4, given the graph of a polynomial …
Factored form: $\boldsymbol{y = -\frac{1}{2}(x+2)^2(x-1)(x-3)}$ Standard form: $\boldsymbol{y = -\frac{1}{2}x^4 + \frac{9}{2}x^2 + 2x - 6}$
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if $f(x) = x^2 - 2$ and $g(x) = x + 4$, find $(f \\circ g)(3)$ and $(g …
a) $(f \circ g)(3) = 47$ b) $(g \circ f)(-3) = 11$
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select the correct answer. what is the range of the function represente…
C. $y\geq1$
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find the value of each variable using sine and cosine. round your answe…
$m \approx 6.7$ $n \approx 10.4$
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find the value of each variable using sine and cosine. round your answe…
$m \approx 6.7$ $n \approx 10.4$
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an object travels along a straight line. the function $s(t) = t^{4}\\co…
$v(t)=4t^3\cos t - t^4\sin t$
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an object travels along a straight line. the function $s(t) = t^{4}\\co…
$v(t)=4t^3\cos t - t^4\sin t$
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6. which one of the representations below corresponds to the solution s…
C) <corresponding graph with shaded region below solid line and above dashed parabola>
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$f(x) = 3x^2 - 6x + 9$. the given equation defines the function $f$. at…
(1, 6)
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25 26 sat simulation grade 11 math part 1 question 17 $12(x - 6) = 4(y …
3
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b. $5enclose{longdiv} {90.5}$
$18.1$
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choose the correct words to fill in the blanks below. hundredths left d…
1. fractional 2. decimal point 3. thousandths 4. tenths 5. hundredths 6. place value 7. right 8. right
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write seven and nine tenths as a decimal number.
7.9
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name________________________ date: __________ period: ____point-slope f…
### Section 1: 1. $y-7=-4(x-2)$ 2. $y-5=-3(x-12)$ 3. $y+5=6(x-4)$ 4. $y+2=3(x+6)$ 5. $y+6=\frac{1}{2}(x-7)$ 6. $y-2=-\frac{3}{4}(x+8)$ ### Section 2 (Graphing Guidelines): 1. For …
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$left(\frac{2}{3} ight)^0$
$\frac{1}{3}$
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unit ii study guide - framework of the constitution spring 26 articles …
1. Representation in the House is based on **state population** 2. An Amendment needs a **three-fourths ($\frac{3}{4}$)** vote of the States to be ratified.
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exit w26l2 name: 1) write an equation of a linear function on the graph…
$y = \frac{3}{2}x - 4$
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how did consumers weaken the economy in the late 1920s?○ consumers only…
B. Consumers bought too many goods they could not afford.
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5 multiple choice 1 point what is the slope of this line?
The slope of the vertical line is undefined.
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what is the slope of line that goes through the points (1, 5) and (4, 1…
B. 5/3
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the graph shown is a translation of the graph of $f(x)=x^{2}$. write th…
$f(x) = (x-3)^2 + 5$
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determine the following for the graph: minimum: □ maximum: □ what is th…
Minimum: -2 Maximum: 2 What is the amplitude? 2 What is the vertical shift from the parent function? 0
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the graph of function $g$ is a translation of the graph of parent funct…
$g(x)=2^x - 5$
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look at this graph: what is the maximum value of this function?
4
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part 5 of 5 a box is to be made out of a rectangular piece of cardboard…
$192 - 4x^2$
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a box is to be made out of a rectangular piece of cardboard that is 12 …
$4x^3 -56x^2 +192x$
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notes w26l2 1) write an equation of a linear function from a graph 2) w…
1. $y=\frac{3}{5}x+5$ 2. $y=\frac{1}{2}x+5$ 3. $y=3x-6$ 4. $y=-\frac{1}{2}x+2$ 5. $y=-4x-6$ 6. $y=-4x-1$
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given that $f(x)$ is a one-to-one function and $f(3)=-4$, $f(-1)=6$, an…
○ 2
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identify the inverse of the function $f(x) = \\frac{2x-7}{7}$. show all…
$\frac{7x+7}{2}$ (corresponding to the third option)
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you will be asked to upload your handwritten work for questions 1 - 3. …
$x^2 - 5$ (Option A)
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graph the given function. $y=2^{x}$ choose the correct graph on the rig…
B. <The graph that is an increasing exponential curve passing through (0,1), approaching the x-axis as x goes to negative infinity>
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1. the parent function $y = \\log(x)$ has which of the following attrib…
An x intercept at (1, 0) D: $(0, \infty)$ R: $y \in \mathbb{R}$ vertical asymptote at x=0
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the graph of $f(x)-y$ is shown in the coordinate plane. which graph sho…
The third option (the bottom-most blue graph, shifted 3 units right from the original) is the correct graph for \(y = f(x-3)\).
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9) label the curves with the correct function names. $f(x) = \\log_{2} …
dashed: $f(x)=\log_2 x$ dotted: $g(x)=\log_3 x$ solid: $h(x)=\log_8 x$
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the function f(x) is shown on the coordinate plane below. y=f(x) which …
$f(x) = x(x + 3)(x - 1)(x - 2)^2$
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religious themes in art and literature what was the purpose of medieval…
### RELIGIOUS THEMES IN ART AND LITERATURE 1. To teach religious doctrine to illiterate people 2. Gothic architecture 3. Pilgrims sharing stories, satirizing medieval society 4. S…
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lem 19 find vertical asymptotes of each curve. if there is no such asym…
$x=0$
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5.10 polynomial long division (my-opm-035) score: 85/100 answered: 6/7 …
The quotient is $x - 4$ The remainder is $2x + 3$
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what is the slope of the linear relationship shown on the graph?
$-2$
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find $lim_{x \to 3} \frac{x + 3}{x^2 - 9}$. enter 1 for $infty$, -1 for…
DNE
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hw 2: problem 17 (1 point) find the limit $lim_{x \\to +\\infty} \\frac…
1
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hw 2: problem 16 (1 point) find the limit $lim_{y \\to -\\infty} \\frac…
0
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identify the parent function of each of the following graphs: graph a: …
Graph A: Square Root Function Graph B: Exponential Function (Decay) Graph C: Cube Root Function Graph D: Quadratic Function
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problem 15 $lim_{x \to infty} -4x^8 + 7x^3 - 5$
$-\infty$
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bill of rights quick check 4 of 5 explain how the first amendment limit…
Congress can pass no law respecting or restricting religion, or laws limiting freedoms of speech, assembly, the press, or to petition the government.
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given the following description, write an equation that meets all the c…
$y = -2\sqrt[3]{x - 13} - 9$ (or y=-2*cbrt(x-13)-9)
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given below is the graph of the cube root parent function, $y = \\sqrt3…
(2,-5)
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select the attribute that does not belong to the equation below: $y = -…
Point of inflection at (-2, 3)
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which equation represents the graph?
$y = -2x - 2$
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which one best describes the graph following function: $y = -2(x + 3)^3…
Cubic Function Point of Inflection: (-3,-1) Decreasing
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math college liberal arts name________ functions introduction date_____…
## Example 1: $f(x)=x+3$ $f(-4) = -1$ $f(-2) = 1$ $f(0) = 3$ $f(2) = 5$ $f(4) = 7$ Domain: All real numbers ($(-\infty, \infty)$) Range: All real numbers ($(-\infty, \infty)$) Inc…
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a cube root function is shown below. $f(x) = -3\\sqrt3{x+2}+4$ which at…
- The graph is decreasing from left to right. - Domain: x=R - Range: y=R - The point of inflection is (-2,4).
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for the given function, state if its increasing (i) or decreasing (d), …
Increasing or Decreasing: D Domain: $\mathbb{R}$ Range: $\mathbb{R}$
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for the given function, state if its increasing (i) or decreasing (d). …
Increasing or Decreasing: I Domain: $\mathbb{R}$ Range: $\mathbb{R}$
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if the following function is of the form : $a \\cdot f(x - h) + k$, sta…
- Function: Cube Root - Point of inflection: $(-4, -6)$ - Factor of vertical dilation $a$: $\frac{1}{4}$ - Increasing or Decreasing: Increasing
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hw 2: problem 12 (1 point) evaluate the limit: $lim_{t \\to 0} \\frac{\…
$7$
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if the following function is of the form : $acdot f(x - h) + k$, state …
- Function: Cubic - Point of inflection: $(3, 2)$ - Factor of vertical dilation $a$: $-1$ - Increasing or Decreasing: Decreasing
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describe the transformations and select the appropriate parent function…
- Shifts down 3 - Shifts left 1 - Reflects over the x-axis - Cubic Function
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describe the transformations and select the appropriate parent function…
- Shifts left 2 - Vertically Stretches by a factor of 4 - Reflects over the x-axis - Cubic Function