$$f(x) = \begin{cases} x^2$ & x \u003c 1 \\ 3 & 1 \leq x \u003c 2 \\ x + 1 & x \geq 2 \end{cases}$$

Question 1

Given the table below, complete the missing values if $$f is an $$even function:

$$x$$      $$-3$$      $$-2$$      $$-1$$      $$0$$      $$1$$      $$2$$      $$3$$

$$f(x)$$      $$21$$      $$-25$$      $$?$$      $$?$$      $$-12$$      $$?$$      $$?$$

Accepted Answer

$$f(-1) = -12,\ f(0) = 0,\ f(1) = -12,\ f(2) = -25,\ f(3) = 21$$

Question 2

Given the piecewise function:

$$
  f(x) = \begin{cases}
    -4x & 	ext{if } x \leq -4 \
    x^3$ + 2 & 	ext{if } -4  2
  \end{cases}
$$

What is $$f(-5) + f(0) + f(3)$$?

Accepted Answer

$$20 + 2 + (-5) = 17$$

Question 3

Evaluate $$-81^{0.5}.$$

Accepted Answer

$$-9$$

Question 4

Simplify $$(9^{3/4})^2$.

Accepted Answer

$$9^{3/2} = 27$

Question 5

Simplify $$\dfrac{8$$^{5/6}$$}{8$$^{1/2}$$}.$$

Accepted Answer

$$8^{1/3}$$

Question 6

Simplify $$27^{5/6}$$ \cdot $$27^{-1/6}.$$

Accepted Answer

$$27^{2/3}$$

Question 7

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 8

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 2x$$

Question 9

Given the graph below, which of the following is the correct piecewise function for $$f(x)$$?

(Refer to the graph with a parabola for $$x \u003c 1$$, a constant for $$1 \leq x \u003c 2$$, and a line for $$x \geq 2.)$$

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \u003c 1 \ 3 & 1 \leq x \u003c 2 \ x + 1 & x \geq 2 \end{cases}$$

Question 10

If $$f(x) is an $$even function and $$f(2) = -25$$, what is $$f(-2)$$?

Accepted Answer

$$-25$$

Question 11

If $$f(x) is an $$odd function and $$f(3) = 7$$, what is $$f(-3)$$?

Accepted Answer

$$-7$$

Question 12

Given $$f(x) = x^2$ + 3x - 2$$, determine if $$f(x) is $$even, odd, or neither.

Accepted Answer

Neither

Question 13

Evaluate $$f(x) at$$ $$x = -4, 0, 3$$ for the piecewise function:

$$
  f(x) = \begin{cases}
    -4x & x \leq -4 \
    x^3$ + 2 & -4  2
  \end{cases}
$$

What is the sum $$f(-4) + f(0) + f(3)$$?

Accepted Answer

$$16 + 2 + (-5) = 13$$

Question 14

Which of the following is the correct simplification for $$(9^{3/4})^2$?

Accepted Answer

$$27$$

Question 15

A function $$f(x) is $$defined as $$f(x) = x^3$ + 2. Is $$this function even, odd, or neither?

Accepted Answer

Neither

Precalculus Review: Even/Odd Functions, Piecewise Functions, and Exponents

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