Guided Practice
Learning Objectives
In this guided practice lesson, you will:
- Apply function notation to evaluate functions at given inputs
- Interpret function values in real-world contexts
- Work with multiple representations of functions
- Build fluency with function operations
Practice Quiz
Work through these 10 problems. Click each question to reveal the answer and explanation.
Question 1: If f(x) = 3x - 7, find f(4).
Answer: f(4) = 5
Solution: Substitute x = 4: f(4) = 3(4) - 7 = 12 - 7 = 5.
Question 2: If g(x) = x² + 2x, find g(-3).
Answer: g(-3) = 3
Solution: Substitute x = -3: g(-3) = (-3)² + 2(-3) = 9 - 6 = 3.
Question 3: If h(x) = 5x + 1 and h(a) = 16, find a.
Answer: a = 3
Solution: Set 5a + 1 = 16. Subtract 1: 5a = 15. Divide by 5: a = 3.
Question 4: If f(x) = 2x - 3 and g(x) = x + 5, find f(g(2)).
Answer: f(g(2)) = 11
Solution: First find g(2) = 2 + 5 = 7. Then f(7) = 2(7) - 3 = 14 - 3 = 11.
Question 5: A function is defined by f(x) = -2x + 10. What is f(0) + f(5)?
Answer: f(0) + f(5) = 10
Solution: f(0) = -2(0) + 10 = 10. f(5) = -2(5) + 10 = 0. Sum: 10 + 0 = 10.
Question 6: Given the table: x = {1, 2, 3, 4}, f(x) = {5, 8, 11, 14}. What is f(3)?
Answer: f(3) = 11
Solution: Look up x = 3 in the table to find f(3) = 11. Note the pattern: f(x) = 3x + 2.
Question 7: If f(x) = |x - 4|, find f(1) + f(7).
Answer: f(1) + f(7) = 6
Solution: f(1) = |1 - 4| = |-3| = 3. f(7) = |7 - 4| = |3| = 3. Sum: 3 + 3 = 6.
Question 8: If f(x) = x² - 4x, for what value(s) of x does f(x) = 0?
Answer: x = 0 or x = 4
Solution: Set x² - 4x = 0. Factor: x(x - 4) = 0. So x = 0 or x = 4.
Question 9: If f(x) = 3x + b and f(2) = 11, find b.
Answer: b = 5
Solution: Substitute: 3(2) + b = 11. Simplify: 6 + b = 11. Subtract 6: b = 5.
Question 10: If f(x) = 4x - 1, find f(2a).
Answer: f(2a) = 8a - 1
Solution: Substitute x = 2a: f(2a) = 4(2a) - 1 = 8a - 1.
Next Steps
- Review any problems that were challenging
- Practice evaluating functions with different input types
- Move on to word problems when ready