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

Shift right 2 units and up 3 units

Question 1

Which of the following is the correct way to factor the quadratic expression $x^2 - 5x + 6$?

Accepted Answer

$(x - 2)(x - 3)$

Question 2

A ball is thrown upward and its height $h$ (in meters) after $t$ seconds is given by $h = -4.9t^2 + 20t + 1$. What is the maximum height reached by the ball?

Accepted Answer

$21.41$ meters

Question 3

Which method can be used to solve the quadratic equation $x^2 + 6x + 5 = 0$?

Accepted Answer

Factoring

Question 4

Complete the square for $x^2 + 8x + 7 = 0$ and solve for $x$.

Accepted Answer

$x = -4 \pm \sqrt{9}$

Question 5

Which of the following is the vertex of the parabola $y = 2(x - 3)^2 + 5$?

Accepted Answer

$(3, 5)$

Question 6

Given the function $f(x) = x^2 - 4x + 3$, what is the axis of symmetry?

Accepted Answer

$x = 2$

Question 7

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

Accepted Answer

$5$

Question 8

Which of the following is the inverse of the function $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \frac{x + 7}{3}$

Question 9

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of items sold (in thousands). What is the maximum profit?

Accepted Answer

$20$ thousand dollars

Question 10

Which of the following is a rational function?

Accepted Answer

$f(x) = \frac{2x + 1}{x - 3}$

Question 11

Solve the inequality $x^2 - 4x < 0$.

Accepted Answer

$0 < x < 4$

Question 12

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

Accepted Answer

Shift right 2 units and up 3 units

Question 13

Which of the following is the solution to the exponential equation $2^x = 16$?

Accepted Answer

$x = 4$

Question 14

What is the domain of the function $f(x) = \frac{1}{x^2 - 9}$?

Accepted Answer

$x \neq 3$ and $x \neq -3$

Question 15

Which of the following is the logarithmic form of the exponential equation $3^x = 81$?

Accepted Answer

$x = \log_3{81}$

Question 16

Solve for $x$: $\log_2{x} = 5$.

Accepted Answer

$x = 32$

Question 17

Which of the following is a solution to the equation $x^3 - 8 = 0$?

Accepted Answer

$x = 2$

Question 18

If $f(x) = x^2$ and $g(x) = x + 1$, what is $f(g(3))$?

Accepted Answer

$16$

Question 19

Which of the following is the correct solution to the quadratic equation $x^2 + 2x - 8 = 0$?

Accepted Answer

$x = -4$ or $x = 2$

Question 20

Which of the following is the correct property of logarithms for $\log_b{(xy)}$?

Accepted Answer

$\log_b{x} + \log_b{y}$

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