# Lesson 6

Symmetry in Equations

### Problem 1

Classify each function as odd, even, or neither.

1. $$f(x)=3x^4+3$$
2. $$f(x)=x^3-4x$$
3. $$f(x)=\frac{1}{x^2+1}$$
4. $$f(x)=x^2+x-3$$

### Solution

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### Problem 2

Here is a graph of a function $$f$$ for $$0 \leq x \leq 5$$.

1. The function $$g$$ is even and takes the same values as $$f$$ for $$0 \leq x \leq 5$$. Sketch a graph of $$g$$.
2. The function $$h$$ is odd and takes the same values as $$f$$ for $$0 \leq x \leq 5$$. Sketch a graph of $$h$$.

### Solution

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### Problem 3

The linear function $$f$$ is given by $$f(x) = mx + b$$. If $$f$$ is even, what can you conclude about $$m$$ and $$b$$

### Solution

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### Problem 4

Here are the graphs of $$y = f(x)$$ and $$y = f(x-1)$$ for a function $$f$$.

Which graph corresponds to each equation? Explain how you know.

### Solution

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(From Unit 5, Lesson 2.)

### Problem 5

Write an expression for two of the graphs in terms of $$f(x)$$.

### Solution

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(From Unit 5, Lesson 3.)

### Problem 6

Here is a graph of the function $$f$$ given by $$f(x) = x^3$$.

1. What happens if you reflect the graph across the $$x$$-axis and then across the $$y$$-axis?
2. Is $$f$$ even, odd, or neither?

### Solution

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(From Unit 5, Lesson 5.)