# Honors Algebra 2: Assignment 13 - Worksheet on Relations

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

1. Find the domain and range: 2. Solution Domain: $$\{ x \in \Re \mid x \geq -2 \} \text{; Range: } \{ y \in \Re \}$$
3. Given the relation $$y = f(x)$$ pictured below, 1. Find the domain and range.
2. Solution Domain: $$x \in \{ -5, -3, -1, 1, 3, 7 \} \text{; Range: }y \in \{ -7, -1, 0, 1, 3, 4 \}$$
3. Evaluate $$f \left( f(-5) \right)$$.
4. Solution 4
5. Evaluate evaluate $$f \left( f(3) \right)$$.
6. Solution Undefined
4. Given the relation $$y = g(x)$$ pictured below 1. Find the domain and range.
2. Solution Domain: $$\{ x \in \Re \}$$; Range: $$\{y \in \Re \mid y \leq 6 \}$$
3. Evaluate $$g \left( g(0) \right)$$.
4. Solution 0
5. Find the domain and range: Solution Domain: $$\{ x \in \Re \mid -6 \leq x \leq 3 \}$$; Range: $$\{ y \in \Re \mid 0 \leq y \leq 8 \}$$
6. Find the domain and range: 7. Solution Domain: $$\{ x \in\Re \mid x \geq -7 \}$$; Range: $$\{ y \in \Re \mid y \leq 8 \}$$
8. Find the domain and range: 9. Solution Domain: $$\{ x \in \Re \mid x \neq 2 \}$$; Range: $${y \in \Re \mid y \neq 7}$$
10. Given $$y = p(x)$$ as in the figure below 1. Find $$p(3)$$
2. Solution 2
3. Find $$p(-8)$$
4. Solution -3
5. Find $$p(2)$$
6. Solution -2
7. For what value(s) of $$x$$ is $$p(x) = 0$$?
8. Solution -5 and $$\displaystyle \frac{13}{5}$$
11. Given $$y = q(x)$$ as in the figure below 1. Find $$q(-2)$$
2. Solution 2
3. Find $$q(7)$$
4. Solution 4
5. For what values of x is $$q(x) = 5$$?
6. Solution -5, -3, and 5
12. Given $$p(x)$$ and $$q(x)$$ as in the two previous problems, evaluate $$p \left( q(-1) \right) .$$
13. Solution $$\displaystyle -\frac{8}{3}$$