Honors Algebra 2: Assignment 13 - Worksheet on Relations



  1. Find the domain and range:
    function
  2. Solution Domain: \( \{ x \in \Re \mid x \geq -2 \} \text{; Range: } \{ y \in \Re \} \)
  3. Given the relation \( y = f(x) \) pictured below,
    Function
    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
    function
    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:
    Function
    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:
    Function
  7. Solution Domain: \( \{ x \in\Re \mid x \geq -7 \} \); Range: \( \{ y \in \Re \mid y \leq 8 \} \)
  8. Find the domain and range:
    Function
  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
    Function
    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
    Function
    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 \(\displaystyle -\frac{8}{3}\)