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

$$f(2) + g(2) = (2 \times 2 + 3) + (2^2$) = 7 + 4 = 11$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the points $$A(2, 3)$$ and $$B(5, 7)$$, what is the distance between them in the Cartesian plane?

Accepted Answer

$$\sqrt{(5-2)^2$ + (7-3)^2$} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Question 3

Which of the following is the correct function notation for 'y is a function of x'?

Accepted Answer

$$y = f(x)$$

Question 4

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

Accepted Answer

$$f(2) + g(2) = (2 	imes 2 + 3) + (2^2$) = 7 + 4 = 11$$

Question 5

Which transformation will shift the graph of $$f(x) up by 4 $$units?

Accepted Answer

$$f(x) + 4$$

Question 6

What is the equation of a circle with center at $$(1, -2)$$ and radius $$3$$?

Accepted Answer

$$(x - 1)^2$ + (y + 2)^2$ = 9$$

Question 7

If $$h(x) = f(x) \cdot g(x)$$, where $$f(x) = x + 1$$ and $$g(x) = x - 1$$, what is $$h(3)$$?

Accepted Answer

$$(3 + 1) \cdot (3 - 1) = 4 \cdot 2 = 8$$

Question 8

Which of the following is NOT a function?

Accepted Answer

A relation where the point $$(2, 3)$$ and $$(2, 5)$$ both exist.

Question 9

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

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 10

A company models its profit $$P as a $$function of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit?

Accepted Answer

$$P(10) = -2(10)^2$ + 40(10) - 100 = -200 + 400 - 100 = 100$$

Question 11

Which of the following describes a vertical stretch of the graph of $$f(x) by a $$factor of $$3$$?

Accepted Answer

$$3f(x)$$

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 13

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 14

If $$f(x) = 2x - 5$$, what is the value of $$x$$ such that $$f(x) = 9$$?

Accepted Answer

$$x = 7$$

Question 15

Which of the following represents a horizontal shift of $$f(x) to $$the right by $$2$$ units?

Accepted Answer

$$f(x - 2)$$

Question 16

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

Accepted Answer

$$f(3) - g(3) = 9 - 6 = 3$$

Question 17

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h(2.04) \approx -4.9(2.04)^2$ + 20(2.04) + 1.5 \approx 21.9$$ meters

Relations and Functions: Precalculus Study Guide

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