Practice Set 1
10 Foundational Questions
This set focuses on function notation, domain, range, piecewise evaluation, intercepts, composition, and simple graph behavior.
Practice Questions
DOK 1 Practice Set: Function Foundations
Use Desmos as a quick support tool while you evaluate functions, read tables, and identify basic graph features.
Question 1
If f(x) = 3x - 1, what is f(4)?
Desmos Move: Type y = 3x - 1 and trace to x = 4 if you want a quick calculator check.
Question 2
Which relation is not a function?
Desmos Move: In Desmos, repeated x-values with different y-values would stack vertically and fail the vertical line test.
Question 3
What is the domain of the table shown?
| x | -1 | 0 | 2 | 4 |
|---|---|---|---|---|
| f(x) | 1 | 3 | 7 | 11 |
Use the x-values for domain and the output at x = 0 for the y-intercept.
Desmos Move: The domain is the set of input values. In a table, those are the x-values.
Question 4
What is the y-intercept of the function shown in the table?
| x | -1 | 0 | 2 | 4 |
|---|---|---|---|---|
| f(x) | 1 | 3 | 7 | 11 |
Use the x-values for domain and the output at x = 0 for the y-intercept.
Desmos Move: The y-intercept happens when x = 0. In a table, find the row where the input is 0.
Question 5
For h(x) = { x + 2 when x < 1; 2x - 3 when x ≥ 1 }, what is h(4)?
Desmos Move: Choose the rule that matches the input first. Since 4 is at least 1, use the second rule.
Question 6
What is the minimum point of y = (x - 2)² + 5?
Desmos Move: Graph y = (x - 2)² + 5 and look for the lowest point of the parabola.
Question 7
If g(x) = 5 - x, what is g(-3)?
Desmos Move: Substitute -3 into the function carefully. The minus sign matters here.
Question 8
On which interval is the graph decreasing?
The graph falls as you move right until the vertex, then it rises.
Desmos Move: Watch what happens as you move left to right. Decreasing means the outputs go down.
Question 9
What is the x-intercept shown in the table?
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| g(x) | 6 | 3 | 0 | -3 |
An x-intercept happens when the output is 0.
Desmos Move: An x-intercept happens when the output is 0. Find the x-value where the table shows y = 0.
Question 10
If f(x) = x + 4 and g(x) = 2x, what is (f ∘ g)(1)?
Desmos Move: For composition, do the inside function first. Start with g(1), then use that output in f.