Function Notation Applications MCR3U Test Unit 1

Function machine relates input to output with a well defined rule. All the operations are performed in an order. Function notation is used to represent output y as g(x) for input x.
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Q1. A ball thrown from the roof of a 60 m tall building reaches the maximum height of 80 m after 2 s.
a. State domain and range
b. Determine equation of the function
c. Find the time when the height of the ball was 75 m.

Q2. Consider the functions f(x) = 2x2 – 3x + 5 and g(x) = 3x – 20.
a. Find 2f(1) – 3
b. When is f(x) = g(x)
c. Find f(2b) – g(1 – b)

Q3. If f(x) = x2 – 2x + 5, determine the input(s) for x whose f(x) = 8.

Q4. Write a function T(x) to model the tax rate described below:
First $50,000 is taxed at 7% and any income above $50,000 is taxed at 15%.

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