Practice Questions

DOK 2 Practice Set: Function Connections

Use Desmos to compare representations, check transformations, and confirm how function features connect across equations, tables, and graphs.

Practice Set 2

10 Connected Questions

This set focuses on matching representations, average rate of change, piecewise rules, inverse functions, transformations, and graph interpretation.

10 questionsDOK 2 review

Question 1

Which equation matches the table shown?

DOK 2

x	0	1	2	3
y	-1	2	5	8

Compare the starting value and the constant change.

Desmos Move: Use the y-intercept first, then check the constant rate of change between table values.

Question 2

What is the average rate of change of f(x) over the interval from x = -1 to x = 3 in the table shown?

DOK 2

x	-1	1	3
f(x)	5	11	17

Average rate of change compares total output change to total input change.

Numeric response

Desmos Move: Use the average rate of change formula: change in output divided by change in input.

Question 3

For p(x) = { 2x + 4 when x < 2; x² - 1 when x ≥ 2 }, what is p(2)?

DOK 2

Desmos Move: Because the input is exactly 2, use the rule that includes x ≥ 2.

Question 4

What is the domain of r(x) = √(x + 5)?

DOK 2

Desmos Move: For a square root, the expression inside the radical must be at least 0.

Question 5

If f(x) = 4x + 1, what is f⁻¹(x)?

DOK 2

Desmos Move: Swap x and y, then solve for y to find the inverse of a linear function.

Question 6

If f(x) = x - 3 and g(x) = x², what is g(f(2))?

DOK 2

Numeric response

Desmos Move: Work inside out. Find f(2) first, then square that result with g.

Question 7

How does y = |x - 2| + 3 compare to y = |x|?

DOK 2

Desmos Move: Look at the expression inside and outside the absolute value separately. Inside changes horizontal position, outside changes vertical position.

Question 8

Function A is shown in the table. Function B is y = 5x - 4. Which function has the greater average rate of change from x = 0 to x = 3?

DOK 2

x	0	1	2	3
A(x)	2	4	6	8

Function A increases by 2 each step of 1 in x.

Desmos Move: For Function A, compare the output change over the interval. For Function B, the slope is already the average rate of change.

Question 9

What is the maximum value of the graph shown?

DOK 2

The maximum value is the y-value of the highest point.

Desmos Move: Look for the highest point on the graph and read its y-value.

Question 10

Use the table shown for f. What is f⁻¹(7)?

DOK 2

x	0	1	3	5
f(x)	1	3	7	11

Inverse values reverse the original input-output pairing.

Numeric response

Desmos Move: For an inverse value, look for the input that produced the output 7 in the original table.