Practice Set 5
10 Mixed Challenge Questions
This set targets common EOC function trouble spots with inverse ideas, average rate comparisons, transformed graphs, domain restrictions, and piecewise models.
Practice Questions
Mixed Practice Set B: Functions
Push into upper-level EOC review with inverse reasoning, domain restrictions, graph interpretation, and steady multi-step function work.
Question 1
What is the domain of q(x) = √(x - 4)?
Desmos Move: For a square root, keep the expression inside the radical at least 0.
Question 2
Use the table shown for f. What is f(0)?
| x | -2 | 0 | 2 |
|---|---|---|---|
| f(x) | -1 | 3 | 7 |
Read the output that matches the given input.
Desmos Move: Look straight above the output row where the input is 0.
Question 3
Which function is one-to-one?
Desmos Move: A one-to-one graph passes the horizontal line test. A non-horizontal line is a strong clue.
Question 4
Function A is shown in the table. Function B passes through (0, 2) and (4, 18). Which function has the greater average rate of change from x = 0 to x = 4?
| x | 0 | 2 | 4 |
|---|---|---|---|
| A(x) | 1 | 5 | 9 |
Function A changes by 8 over the full interval from 0 to 4.
Desmos Move: Compute the rate for the table, then compare it to the slope from the two graph points.
Question 5
A student says, "If a function is not one-to-one, then it cannot have an inverse relation at all." Which response is best?
Desmos Move: Swapping x and y still creates an inverse relation. The question is whether that new relation passes the vertical line test.
Question 6
A streaming service charges $8 for the first month and $3 per month after that. If C(m) = { 8 when m = 1; 8 + 3(m - 1) when m > 1 }, what is C(5)?
Desmos Move: Use the second rule because the input is greater than 1, then count how many extra months are being charged.
Question 7
Which equation best matches the graph shown?
The graph is reflected downward and shifted right 2 and up 5.
Desmos Move: Use the vertex and the opening direction together. Those two clues usually narrow the choice quickly.
Question 8
If f(x) = 3x - 7, what is f⁻¹(11)?
Desmos Move: Ask yourself what input would make the original function output 11.
Question 9
Which representation shows a function with a constant rate of change?
Desmos Move: Constant rate of change means the first differences stay the same.
Question 10
If p(x) = 5x - 2, what is p⁻¹(18)?
Desmos Move: Set the original function equal to 18 and solve for x.