Q: Which transformation occurs when the graph of $f(x) = x^2$ is changed to $g(x) = (x-3)^2 + 2$?

Shift right 3 units and up 2 units

Question 1

Which of the following best describes the domain of the function $f(x) = \sqrt{2x - 8}$?

Accepted Answer

$x \geq 4$

Question 2

A company’s revenue $R$ (in thousands of dollars) is modeled by the function $R(x) = 50x - x^2$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $625$ thousand dollars at $x = 25$ thousand units.

Question 3

Given $f(x) = 2x + 3$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$(f \circ g)(2) = 11$

Question 4

Which of the following equations represents a function whose graph is a parabola opening downward?

Accepted Answer

$y = -3x^2 + 2x - 1$

Question 5

If $f(x) = \ln(x-1)$, what is the domain of $f$?

Accepted Answer

$x > 1$

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $P$ after $t$ hours?

Accepted Answer

$P(t) = 200 \cdot 3^{t/4}$

Question 7

Solve the equation $2^{x+1} = 16$ for $x$.

Accepted Answer

$x = 3$

Question 8

Which of the following is the inverse of the function $f(x) = 5x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x+7}{5}$

Question 9

Which of the following best describes the range of the function $f(x) = \dfrac{1}{x-2}$?

Accepted Answer

All real numbers except $0$

Question 10

A radioactive substance decays according to $A(t) = A_0 e^{-0.05t}$, where $t$ is in years. If the initial amount is $100$ grams, how much remains after $20$ years (rounded to the nearest gram)?

Accepted Answer

$37$ grams

Question 11

Which of the following is NOT a function?

Accepted Answer

A relation where $x = 2$ maps to both $y = 3$ and $y = 5$

Question 12

Solve the inequality $3x - 5 < 7$.

Accepted Answer

$x < 4$

Question 13

Which transformation occurs when the graph of $f(x) = x^2$ is changed to $g(x) = (x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 14

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f + g)(2)$?

Accepted Answer

$(f + g)(2) = 7$

Question 15

Which of the following is the solution set for $|2x - 3| = 7$?

Accepted Answer

$x = 5$ or $x = -2$

Question 16

A car’s value depreciates exponentially according to $V(t) = 20000 \cdot (0.85)^t$, where $t$ is the number of years after purchase. What is the value of the car after 3 years (rounded to the nearest dollar)?

Accepted Answer

$12250$

Question 17

Which of the following is the solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3, y = 2$

Question 18

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x - 4)(x - 5)$

Question 19

If $f(x) = \dfrac{2x}{x+1}$, what is the value of $f^{-1}(2)$?

Accepted Answer

$f^{-1}(2) = 2$

Question 20

Which of the following best describes the end behavior of the polynomial $f(x) = -2x^3 + 5x^2 - x + 7$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o -\infty$

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