# 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.

\(x\) | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|---|---|---|---|

\(f(x)\) | 2 | 8 | 10 | -1 | 0 |

Complete the table.

### Problem 3

Here is the graph of \(y = x -2\).

- Is there a vertical translation of the graph that represents an even function? Explain your reasoning.
- 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.

- \(\frac14 \sqrt[3]{d}=15\)
- \(\text- \sqrt[3]{e}=7\)
- \(\sqrt[3]{f-5}+2=4\)

### Problem 6

Here is the graph of \(f\).

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

### Problem 7

The graph models Priya's heart rate before, during, and after a run.

- What was Priya's approximate heart rate before and after the run?
- About how high did Priya's heart rate get during the run?
- Sketch what the graph would look like if Priya went for the run three hours later.