Q: A function is said to be even if:

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

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

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

Question 1

Which of the following is the correct domain of the function $$g(x) = \frac{x+8}{x^2$-1}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, 1) \cup (1, \infty)$$

Question 2

Given the equation $$4x + 6y = 120$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$30$$, $$y-$$intercept: $$20$$

Question 3

Evaluate $$f(x) = x^2$ + 2x + 1 at$$ $$x = -1.$$

Accepted Answer

$$0$$

Question 4

For the function $$f(x) = x^2$ + 2x + 1$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 - 2x + 1$

Question 5

A function is said to be even if:

Accepted Answer

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

Question 6

Given the piecewise function $$f(x) = \begin{cases} x-5 & x \u003e 0 \ 3 & x \leq 0 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$-3$$

Question 7

Which transformation describes the function $$f(x) = 4 - (x+1)^2$ compared to g(x$$) = $$x^2$$?

Accepted Answer

Shift left 1 unit, reflect over the $$x-$$axis, shift up 4 units

Question 8

Which of the following equations represents a function that is shifted 7 units right, reflected about the $$x-$$axis, and shifted 9 units down from $$f(x) = \sqrt{x}$$?

Accepted Answer

$$f(x) = -\sqrt{x-7} - 9$$

Question 9

Given the points $$(-5, -1)$$ and $$(3, 8)$$, what is the slope of the line passing through them?

Accepted Answer

$$\frac{9}{8}$$

Question 10

Which of the following is the correct equation in slope-intercept form for the line passing through $$(-5, -1)$$ and $$(3, 8)$$?

Accepted Answer

$$y = \frac{9}{8}x + \frac{41}{8}$$

Question 11

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

Accepted Answer

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

Question 12

Given the function $$f(x) = x$$ for $$x \geq 2$$ and $$f(x) = 2$$ for $$x \u003c 2$$, what is $$f(1)$$?

Accepted Answer

$$2$$

Question 13

Which of the following describes the transformation from $$f(x) to$$ $$g(x) = f(2x)$$?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{2}$$

Question 14

Which of the following intervals describes where the function in the graph is increasing?

Accepted Answer

$$(-4, -3)$$

Question 15

Which of the following intervals describes where the function in the graph is decreasing?

Accepted Answer

$$(-3, -2)$$

Question 16

Which of the following best describes the symmetry of the function shown in the graph with points $$(-2, -3)$$, $$(0, 1)$$, and $$(2, 3)$$?

Accepted Answer

Neither even nor odd

Question 17

Which of the following is the correct graph for the piecewise function $$f(x) = \begin{cases} x-5 & x \u003e 0 \ 3 & x \leq 0 \end{cases}$$?

Accepted Answer

A graph with a horizontal line at $$y=3$$ for $$x \leq 0$$ and a line with slope 1, $$y = x-5$$, for $$x \u003e 0.$$

Precalculus Study Guidance: Functions, Graphs, Domains, and Transformations

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