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

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

Q: Which of the following is a rational function?

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

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

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

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 $$x^2 - 4x$$ \u003c 0$$.

Accepted Answer

$$0 \u003c x \u003c 4$$

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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