Q: If $$f(x) is an $$even function, which of the following must be true?

$$f(-x) = f(x)$$ \text{ for all } x$

Question 1

Which of the following numbers is an irrational number?

Accepted Answer

$$\sqrt{5}$$

Question 2

Given the points $$(2, 4)$$ and $$(0, -3)$$, what is the slope of the line passing through them?

Accepted Answer

$$\frac{4 - (-3)}{2 - 0} = \frac{7}{2}$$

Question 3

Which interval notation represents all real numbers $$x$$ such that $$-2 \u003c x \leq 5$$?

Accepted Answer

$$(-2, 5]$$

Question 4

If $$f(x) = 2x + 1$$, what is the zero of $$f$$?

Accepted Answer

$$x = -\frac{1}{2}$$

Question 5

A company has a fixed cost of $$40,000$$ and a variable cost of $$3$$ per T-shirt. If the T-shirts sell for $$10$$ each, how many must be sold to break even?

Accepted Answer

$$\frac{40,000}{10 - 3} = 5,714$$

Question 6

Which of the following is the equation of a line passing through $$(1, 3)$$ and parallel to $$x - y + 4 = 0$$?

Accepted Answer

$$x - y + 2 = 0$$

Question 7

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

Accepted Answer

$$(f \circ g)(x) = (2x - 1)^2$

Question 8

If $$f(x) = |x - 4|$$, what is the solution set for $$f(x) = 5$$?

Accepted Answer

$$x = 9 or$$ $$x = -1$$

Question 9

Which of the following describes the transformation from $$f(x) = x^2$ to g(x) = 2(x$$ - $$1)^2 + 3$?

Accepted Answer

Shift right 1 unit, vertical stretch by factor 2, shift up 3 units

Question 10

Suppose you invest $$50,000 in $$stocks and bonds. Stocks pay $$6\%$$ annually and bonds pay $$2\%$$ annually. If the annual interest income is $$1,892$$, how much was invested in stocks?

Accepted Answer

$$x = 33,800$$

Question 11

Which of the following is the domain of $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$[3, \infty)$$

Question 12

If $$f(x) = x^3$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 13

Which of the following is the range of $$f(x) = |x|$$ for $$x \in [-2, 1]$$?

Accepted Answer

$$[0, 2]$$

Question 14

Given the function $$f(x) = 3x - 5$$, what is the solution set for $$2 \leq f(x) \u003c 18$$?

Accepted Answer

$$\left[\frac{7}{3}, 7\right)$$

Question 15

Which of the following is the difference quotient for $$f(x) = x^2$ - 2x + 7$$?

Accepted Answer

$$\frac{(x + h)^2$ - 2(x + h) + 7 - (x^2$ - 2x + 7)}{h}$$

Question 16

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for all } x$

Question 17

Which of the following is the correct interval notation for the solution to $$|x - 3| \u003c 10$$?

Accepted Answer

$$(-7, 13)$$

Question 18

A line passes through $$(2, 4)$$ and is perpendicular to $$x = 7. $$What is its equation?

Accepted Answer

$$y = 4$$

Question 19

Which of the following is the correct interpretation of the vertical line test?

Accepted Answer

If a vertical line intersects a graph at more than one point, the relation is not a function.

Precalculus Study Guide: Functions, Equations, and Graphs

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