Question 1

Given the graph of $$y = f(x)$$ shown, what is the equation of the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 2

Which of the following statements best describes the Horizontal Line Test?

Accepted Answer

A function passes the Horizontal Line Test if every horizontal line intersects the graph at most once.

Question 3

What is the distance between the points $$(-1, 4)$$ and $$(3, -2)$$?

Accepted Answer

$$\sqrt{52}$$

Question 4

What is the midpoint of the segment with endpoints $$(1, 2)$$ and $$(7, -3)$$?

Accepted Answer

$$(4, -0.5)$$

Question 5

Write the standard form of the equation of a circle centered at $$(0, 0)$$ with radius $$4.$$

Accepted Answer

$$x^2$$ + $$y^2 = 16$

Question 6

Given the equation $$(x - 2)^2$ + (y + 4)^2$ = 9$$, what is the center and radius of the circle?

Accepted Answer

Center $$(2, -4)$$, radius $$3$$

Question 7

Complete the square to write $$x^2$$ + $$y^2 + 4x - 6y - 23 = 0$ in standard form.

Accepted Answer

$$(x + 2)^2$ + (y - 3)^2$ = 36$$

Question 8

For the quadratic function $$f(x) = -2(x - 3)^2$ + 8$$, what is the vertex?

Accepted Answer

$$(3, 8)$$

Question 9

For $$f(x) = -x^2$ - 2x + 1$$, what is the direction in which the parabola opens?

Accepted Answer

Downward

Question 10

For the rational function $$f(x) = \frac{x + 7}{x^2$ + 1}$$, what are the vertical asymptotes?

Accepted Answer

None

Question 11

For $$f(x) = \frac{2x^2$ + 9x + 8}{x^2$ - 10}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 12

Solve the inequality $$\frac{2x}{x + 1} \geq 1. $$What is the solution set?

Accepted Answer

$$x \leq -1 or$$ $$x \geq 1$$

Question 13

For $$f(x) = -3x^2$ + 6x - 13$$, what is the maximum value of the function?

Accepted Answer

$$-4$$

Question 14

An archer’s arrow follows $$f(x) = -0.005x^2$ + 0.15x + 5. $$What is the maximum height reached by the arrow?

Accepted Answer

$$5.225$$ feet

Question 15

For $$f(x) = \frac{2x^2$}{(x - 3)(x - 2)}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 3$$ and $$x = 2$$

Question 16

For $$f(x) = \frac{2x}{x^2$ - 2x + 1}$$, what is the y-intercept?

Accepted Answer

$$0$$

Question 17

For $$f(x) = \frac{x - 1}{x^2$ - 9}$$, what is the domain?

Accepted Answer

All real numbers except $$x = 3$$ and $$x = -3$$

Question 18

Solve the inequality $$\frac{x + 1}{x + 3} \u003c 2. $$What is the solution set?

Accepted Answer

$$x  -1$$

Finding the Inverse of a Function from Its Graph

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