Practice Set 4
10 Mixed Functions Questions
This set mixes easy, medium, and challenging questions about evaluating functions, inverse ideas, transformations, average rate of change, and modeling.
Practice Questions
Mixed Practice Set A: Functions
Move between quick checks, tables, graph reading, and function rules so you can practice the same kind of switching the EOC expects.
Question 1
If f(x) = 1 - 2x, what is f(-2)?
Desmos Move: Substitute -2 carefully. A negative input can change the sign of the middle step.
Question 2
Which relation represents a function?
Desmos Move: A function can repeat outputs, but it cannot repeat an input with a different output.
Question 3
What is the average rate of change of the table shown from x = 0 to x = 4?
| x | 0 | 2 | 4 |
|---|---|---|---|
| f(x) | 1 | 9 | 17 |
Compare the outputs at the endpoints of the interval.
Desmos Move: Use the outputs at the two endpoints. Average rate of change is total output change over total input change.
Question 4
For m(x) = { 3x when x ≤ 1; x + 4 when x > 1 }, what is m(3)?
Desmos Move: The condition tells you which rule to use. Since 3 is greater than 1, use the second rule.
Question 5
How does y = (x + 3)² - 1 compare to y = x²?
Desmos Move: Look at the sign inside the parentheses for horizontal movement and the outside number for vertical movement.
Question 6
Function A is shown in the table. Function B is y = 2x + 1. Which function has the greater y-intercept?
| x | 0 | 1 | 2 |
|---|---|---|---|
| A(x) | 5 | 7 | 9 |
Function A starts at 5 when x = 0.
Desmos Move: A y-intercept happens when x = 0. Compare the output at x = 0 for each function.
Question 7
Use the table shown for f. What is f⁻¹(3)?
| x | 0 | 2 | 4 |
|---|---|---|---|
| f(x) | -1 | 3 | 7 |
Inverse questions send an output back to its original input.
Desmos Move: An inverse reverses the original pair. Look for the input whose output is 3.
Question 8
Which equation best matches the graph shown?
Match the graph's vertex and opening direction to the equation.
Desmos Move: Find the vertex first. That tells you the horizontal and vertical shifts.
Question 9
A revenue graph reaches its highest point when x = 120 tickets are sold. Which statement best uses the model?
Desmos Move: In context, the x-value of the maximum point often gives the best recommendation.
Question 10
If f(x) = 2x + 1 and g(x) = x², what is (g ∘ f)(2)?
Desmos Move: Composition means do f first, then use that output in g.