# Lesson 5

Some Functions Have Symmetry

• Let's look at symmetry in graphs of functions

### Problem 1

Classify each function as odd, even, or neither.

### Problem 2

The table shows the values of an even function $$f$$ for some inputs.

 $$x$$ $$f(x)$$ -4 -3 -2 -1 0 1 2 3 4 2 8 10 -1 0

Complete the table.

### Problem 3

Here is the graph of $$y = x -2$$.

1. Is there a vertical translation of the graph that represents an even function? Explain your reasoning.
2. Is there a vertical translation of the graph that represents an odd function? Explain you reasoning.

### Problem 4

The function $$f$$ is odd. Which statements must be true? Select all that apply.

A:

If $$f(5) = 2$$, then $$f(\text-5) = 2$$.

B:

If $$f(5) = 3$$, then $$f(\text-5) = \text-3$$.

C:

Reflection over the $$y$$-axis takes the graph of $$f$$ to itself.

D:

Reflecting $$f$$ across both axes takes the graph of $$f$$ to itself.

E:

$$f(0) = 0$$

### Problem 5

Find the exact solution(s) to each of these equations, or explain why there is no solution.

1. $$\frac14 \sqrt{d}=15$$
2. $$\text- \sqrt{e}=7$$
3. $$\sqrt{f-5}+2=4$$
(From Unit 3, Lesson 8.)

### Problem 6

Here is the graph of $$f$$.

1. Graph the function $$g$$ given by $$g(x) = \text-f(x)$$.
2. Graph the function $$h$$ given by $$h(x) = f(\text-x)$$.