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Function Notation and Evaluation
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Function Notation and Evaluation
Substitute each input into the function rule and simplify. Show your working where space is provided. For multiple-select questions, choose every correct answer.
Understanding Function Notation
1.What does p(6) = 15 tell you?
- The function p is multiplied by 6 to get 15.
- An input of 6 gives an output of 15 in function p.
- The function p has 6 inputs and 15 outputs.
- The input is 15 and the output is 6.
2.If r(x) = 3x − 2, what is r(5)?
- 10
- 11
- 13
- 15
3.For s(n) = n² + 1, find s(−3).
- −8
- −2
- 8
- 10
4.Write every expression below that is in function notation: a(x) = 2x + 7; y = 4x − 3; M(k) = k² − 5; 5x + y = 9.
Function Evaluation Practice
5.Let f(x) = 5x + 2. Find each value: f(0), f(4), and f(−2).
6.Given g(x) = 2x² − 3x + 4, evaluate g(3). Show your substitution and simplification.
7.A bike rental shop charges a $6 starting fee plus $4 for each hour rented. The cost for h hours is B(h) = 6 + 4h. Find B(5), then state what B(5) means.
Function Notation in Context
8.A model rocket’s height is H(t) = −16t² + 48t + 4 feet, where t is the number of seconds after launch. Calculate H(1) and H(2).
9.A streaming subscription costs $12 per month, with an additional $0.50 for each movie rented. Write a function C(m) for the monthly cost with m movie rentals. Then find C(8) and explain what the value represents.
10.In one sentence, explain what f(7) = 20 tells you about the function f.
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