Q: Which of the following best describes the end behavior of $f(x) = 200x^{10} + 4.5x^5 - 456$?

$f(x) \to \infty$ as $x \to \infty$, $f(x) \to \infty$ as $x \to -\infty$

Q: Given $f(x) = (x-1)(x-3)(x+1)^2$, what is the end behavior of $f(x)$?

$f(x) \to \infty$ as $x \to \infty$, $f(x) \to \infty$ as $x \to -\infty$

Question 1

Given the function $f(x) = x^2 + 6x - 2$, what are the coordinates of the vertex of the parabola?

Accepted Answer

$(-3, -11)$

Question 2

For the function $f(x) = x^2 + 6x - 2$, what are the exact $x$-intercepts in simplified form?

Accepted Answer

$x = -3 \pm \sqrt{11}$

Question 3

Given the function $f(x) = |x|$, what is the equation for $g(x)$, which is the graph of $f(x)$ reflected across the $x$-axis and stretched horizontally by a factor of 2?

Accepted Answer

$g(x) = -\frac{1}{2}|x|$

Question 4

A company models its revenue $R(x)$ as a function of the number of calculators sold, $x$, by $R(x) = x \left( -\frac{1}{2}x + 100 \right)$. What number of calculators maximizes the revenue?

Accepted Answer

$x = 100$

Question 5

Given the rational function $f(x) = \frac{x^2 + 6x + 5}{2x^2 + 7x + 5}$, what are the equations of the vertical asymptotes?

Accepted Answer

$x = -1, x = -\frac{5}{2}$

Question 6

For the function $f(x) = \sqrt{x^2 + 5x + 2}$, what is the domain?

Accepted Answer

$(-\infty, -2] \cup [-1, \infty)$

Question 7

Given $f(x) = (x-1)(x+2)^2$, for which values of $x$ is $\frac{(x-1)(x+2)^2}{x(x-3)} \leq 0$?

Accepted Answer

$[-2, 0) \cup (0, 3)$

Question 8

A polynomial $f(x)$ has degree 3, crosses the $x$-axis at $(2,0)$, and touches the $x$-axis at $(-3,0)$. Which of the following could be its equation?

Accepted Answer

$f(x) = (x-2)(x+3)^2$

Question 9

Given the function $f(x) = (x-1)(x-3)(x+1)^2$, what is the $y$-intercept?

Accepted Answer

$f(0) = -3$

Question 10

Which transformation describes $h(x) = 5|x-2| + 3$ relative to $f(x) = |x|$?

Accepted Answer

Shifted right 2, stretched vertically by 5, shifted up 3

Question 11

Given the function $f(x) = (x-1)(x+2)^2$, what is the multiplicity of the zero at $x = -2$ and does the graph cross or touch the $x$-axis at this point?

Accepted Answer

Multiplicity 2, touches the $x$-axis

Question 12

Which of the following best describes the end behavior of $f(x) = 200x^{10} + 4.5x^5 - 456$?

Accepted Answer

$f(x) 	o \infty$ as $x 	o \infty$, $f(x) 	o \infty$ as $x 	o -\infty$

Question 13

Given the rational function $f(x) = \frac{x^2 + 6x + 5}{2x^2 + 7x + 5}$, what is the equation of the horizontal asymptote?

Accepted Answer

$y = \frac{1}{2}$

Question 14

A scatterplot of data shows a pattern that curves upward and then levels off. Which type of model is most appropriate for this data?

Accepted Answer

Neither

Question 15

If $g(x) = -f(x+2)$, which transformation is applied to $f(x)$ to obtain $g(x)$?

Accepted Answer

Reflected across the $x$-axis and shifted left 2

Question 16

Given $f(x) = (x-1)(x-3)(x+1)^2$, what is the end behavior of $f(x)$?

Accepted Answer

$f(x) 	o \infty$ as $x 	o \infty$, $f(x) 	o \infty$ as $x 	o -\infty$

Question 17

For the function $f(x) = \sqrt{x^2 + 5x + 2}$, which of the following intervals is NOT included in the domain?

Accepted Answer

$(-2, -1)$

Question 18

Given the function $f(x) = (x-1)(x+2)^2$, what is the $x$-intercept with the highest multiplicity?

Accepted Answer

$x = -2$

Question 19

If $h(x) = \frac{1}{2}f(x) - 1$, what transformation is applied to $f(x)$ to obtain $h(x)$?

Accepted Answer

Compressed vertically by a factor of $\frac{1}{2}$ and shifted down 1

College Algebra: Functions, Graphs, Transformations, and Applications – Study Guide

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