Question 1

Which of the following is the correct simplification of $$\frac{3}{4} 	imes \frac{8}{9}$$?

Accepted Answer

$$\frac{2}{3}$$

Question 2

What is the result of $$2^3$$ 	imes $$2^{-5}$$ using the laws of exponents?

Accepted Answer

$$2^{-2}$$

Question 3

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

Accepted Answer

$$x \geq 2$$

Question 4

Given the function $$f(x) = x^2$, which transformation represents g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 5

If $$f(x) = x^3$ and f(-x) = -f(x$$)$$, what type of symmetry does f(x$$)$$ have?

Accepted Answer

Odd symmetry (origin symmetry)

Question 6

Convert $$120^{\circ} to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 7

Given $$\sin(	heta) = \frac{1}{2}$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{5\pi}{6}$$

Question 8

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

Accepted Answer

$$(x-3)(x+3)$$

Question 9

What is the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$2$$

Question 10

If $$f(x) = |x|$$, which statement is true about its symmetry?

Accepted Answer

$$f(x) is $$even

Question 11

Which of the following is the correct simplification of $$\frac{2x^2$}{4x}$$?

Accepted Answer

$$\frac{x}{2}$$

Question 12

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

Accepted Answer

$$9$$

Question 13

Which of the following is the correct equation of a line with slope $$-3$$ passing through $$(1, 4)$$?

Accepted Answer

$$y - 4 = -3(x - 1)$$

Question 14

If $$	an(	heta) = \frac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

$$\frac{3}{5}$$

Question 15

Which of the following is the correct factorization of $$x^3 + 8$?

Accepted Answer

$$(x + 2)(x^2$ - 2x + 4)$$

Question 16

What is the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 17

Which of the following is the correct simplification of $$\frac{5}{x} + \frac{3}{x}$$?

Accepted Answer

$$\frac{8}{x}$$

Question 18

If $$f(x) = x^2$ and g(x$$) = $$-x^2$$, which statement is true about their graphs?

Accepted Answer

The graph of $$g(x) is a $$reflection of $$f(x)$$ across the x-axis.

Precalculus Foundations: Algebra, Functions, and Trigonometry Study Notes

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