ACT Math — Functions — Drill 4

About This Drill

ACT Math — Functions — Drill 4 is a Math practice drill covering Functions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This drill covers interpreting key features of function graphs, real-world piecewise functions, numerical function composition, transformations including reflections and vertical stretches, and the inverse relationship between logarithmic and exponential functions.

Questions in This Drill

1. A linear function f passes through the points (0, −4) and (2, 0). What is f(6)?
2. A cell phone plan charges $30 per month for up to 5 gigabytes (GB) of data, plus $10 for each additional GB beyond 5. Which of the following piecewise functions gives the monthly cost C(g), in dollars, for g gigabytes of data used?
3. The table below gives values for functions f and g.
   x        1    2    3    4    5
   f(x)    3    5    2    1    4
   g(x)    4    1    5    2    3
   What is the value of f(g(3))?
4. The graph of f(x) is transformed to produce the graph of g(x) = −3f(x) + 2. Which of the following describes the transformation?
5. If f(x) = 3^x and g(x) = log₃(x), what is f(g(81))?