Practice Set 3
10 Strategic Questions
This set focuses on inverse reasoning, piecewise modeling, average rate of change, transformations, one-to-one functions, and context-based decisions.
Practice Questions
DOK 3 Practice Set: Function Reasoning
Use Desmos strategically to test claims, compare representations, and justify multi-step choices in richer function questions.
Question 1
A student says, "Every function has an inverse that is also a function." Which response best corrects the claim?
Desmos Move: Use the horizontal line test in Desmos. If a horizontal line hits more than once, the inverse will not be a function.
Question 2
A student says, "If f(2) = 5, then f⁻¹(2) = 5." Which response is best?
Desmos Move: Inverse functions reverse inputs and outputs. A point (2, 5) on f becomes (5, 2) on f⁻¹.
Question 3
A parking garage charges $6 for up to 2 hours and $2 for each additional hour after that. Which piecewise function could model the cost C(h)?
Desmos Move: Think about what the cost should be right at 2 hours, then build the second rule from that starting point.
Question 4
If T(c) = 1.8c + 32 converts Celsius to Fahrenheit and C(f) = (f - 32) / 1.8 converts Fahrenheit to Celsius, what is C(T(15))?
Desmos Move: Use the inside function first. These two rules undo each other.
Question 5
Function A is shown in the table. Function B is shown in the graph. Which function has the greater average rate of change from x = 0 to x = 4?
| x | 0 | 2 | 4 |
|---|---|---|---|
| A(x) | 2 | 6 | 10 |
Function B passes through the points (0, 1) and (4, 13).
Desmos Move: For the table, compare the outputs at the two endpoints. For the graph, read the two endpoint values and compute the slope.
Question 6
Which domain makes the most sense for the function A(s) = s² when s is the side length of a square in feet?
Desmos Move: Context matters. Side lengths cannot be negative.
Question 7
Which equation best matches the graph shown?
The graph is reflected downward and shifted right 1 and up 4.
Desmos Move: Look for the vertex first, then decide whether the graph opens up or down.
Question 8
For f(x) = x² + 4x + 1, what is the average rate of change from x = -1 to x = 3?
Desmos Move: Find f(-1) and f(3), then divide the output change by the input change.
Question 9
Which statement best explains why the graph shown is one-to-one?
Each output appears only once, so the inverse can also be a function.
Desmos Move: The horizontal line test is a fast way to decide whether an inverse will also be a function.
Question 10
A profit graph reaches its highest point at x = 18. Which recommendation best uses the model?
Desmos Move: In a real-world graph, the x-value of the highest point often gives the best recommendation.