Piecewise and step functions: evaluate and graph

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Esme's scooter fare is f(x) = x + 2 when x < 3 and f(x) = 2x when x ≥ 3. Since 5 is at least 3, use 2x. What is f(5)?

   10
2. 2.

   Kira's price is f(x) = 10 − x when x < 4, f(x) = 2x + 1 when x ≥ 4. Since 7 is at least 4, use 2x + 1. What is f(7)?

   15
3. 3.

   Up to 1 hour $3; up to 2 hours $5; up to 3 hours $7; up to 4 hours $9. Milo parks a car at a lot. What does 1.5 hours cost?

   $5
4. 4.

   Up to 1 oz $0.50; up to 2 oz $0.75; up to 3 oz $1.00; up to 4 oz $1.25. Noah mails a letter that weighs exactly 2 ounces. What does the stamp cost?

   $0.75
5. 5.

   Up to 1 hour $3; up to 2 hours $5; up to 3 hours $7; up to 4 hours $9. Pia parks a bus at the same lot. What does 3.2 hours cost?

   $9
6. 6.

   Up to 1 oz $0.50; up to 2 oz $0.75; up to 3 oz $1.00; up to 4 oz $1.25. Ren mails a stack of paper that weighs exactly 3 ounces. What does the stamp cost?

   $1
7. 7.

   Tala scores a game with f(x) = 3x when x ≤ 2 and f(x) = x + 4 when x > 2. Which rule do we use for x = 2?

   • x + 4, because 2 is where the rule changes
   • Both rules, then add them
   • 3x, because x ≤ 2 includes 2
8. 8.

   Zee counts coins with f(x) = x + 1 when x < 5 and f(x) = 2x when x ≥ 5. Which rule do we use for x = 5?

   • Both rules, then add them
   • 2x, because x ≥ 5 includes 5
   • x + 1, because 5 is where the rule changes
9. 9.

   Ari drums for a game with f(x) = 2x when x ≤ 3 and f(x) = x + 6 when x > 3. Which rule do we use for x = 3?

   • x + 6, because 3 is where the rule changes
   • 2x, because x ≤ 3 includes 3
   • Both rules, then add them
10. 10.

    Bo flies kites with f(x) = 10 − x when x < 6 and f(x) = 3x when x ≥ 6. Which rule do we use for x = 6?

    • 10 − x, because 6 is where the rule changes
    • Both rules, then add them
    • 3x, because x ≥ 6 includes 6