Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
They also compute and interpret average rates of change (F-IF.B.6) and compare functions given in different forms (F-IF.C.9). The last six problems are multi-step contexts such as stock prices, phone plans and profit.
Standards: F-IF.B.4, F-IF.B.6, F-IF.C.9 · Level: Grade 9 Algebra 1
Problem 2 Intercepts with a negative slope ★★★
Find the intercepts of y = −3x + 12.
Problem 3 Increasing or decreasing ★★★
Is f(x) = −4x + 1 increasing or decreasing? Explain.
Problem 4 Rate from a table ★★★
A function has this table:
| x | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| f(x) | 10 | 16 | 22 | 28 |
Is it increasing or decreasing? Find the average rate of change from x = 2 to x = 6.
Problem 5 Reading a parabola ★★★
Read off where the graph crosses each axis and where it is lowest.
Problem 6 Positive and negative intervals ★★★
For the graph in Problem 5, state where the function is positive and where it is negative.
Problem 7 Increasing, decreasing, extremes ★★★
Find the intervals of rise and fall, and each relative maximum and minimum point.
Problem 8 Rate of change of a quadratic ★★★
Compute how fast f(x) = x2 − 6x + 5 changes on average as x moves from 2 to 6.
Problem 9 Rate with a negative input ★★★
Starting at an input of −4 and ending at an input of 3, what is the average rate of change of f(x) = x2 − 11?
Problem 10 Rate from a graph ★★★
The graph shows g(x) = 0.5x2. Use the two marked points to find the slope of the secant line between them.
Problem 11 End behavior ★★★
Describe the end behavior of (a) f(x) = −7x + 3 and (b) g(x) = −x2 + 10.
Problem 12 Symmetry of a parabola ★★★
The graph of f(x) = (x − 3)2 − 2 is symmetric about the vertical line x = 3. If (0, 7) is on the graph, which point at the same height is its mirror image? Verify with the equation.
Problem 13 Compare an equation and a table ★★★
Function f(x) = 4x + 1. Function g has the table:
| x | 1 | 2 | 3 |
|---|---|---|---|
| g(x) | 6 | 11 | 16 |
Which function climbs faster per unit of x? Write a rule for g.
Problem 14 Balloon flight ★★★
The graph shows a balloon’s altitude. State when it is increasing, constant and decreasing, the greatest altitude, and the average rate of change from 0 to 10 minutes and from 20 to 35 minutes.
Problem 15 Bike trip table ★★★
The table shows the distance of a cyclist from the start.
| Hours | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Miles | 0 | 14 | 30 | 44 | 60 |
Find the average rate of change on 0 to 2 hours, 2 to 4 hours and 1 to 3 hours, and then on 0 to 1 hour. Is the rate constant?
Problem 16 Stock price ★★★
A stock’s price P(t) in dollars at week t has P(0) = 48, P(4) = 60 and P(10) = 42. Find the average rate of change from week 0 to 4, from 4 to 10 and from 0 to 10, and interpret each.
Problem 17 Two phone plans ★★★
Plan A: C(m) = 18 + 0.12m dollars for m minutes. Plan B has this table:
| Minutes | 100 | 200 | 300 |
|---|---|---|---|
| Cost (dollars) | 28 | 36 | 44 |
Which plan grows faster? Find each cost at 500 minutes and the number of minutes where the plans cost the same.
Problem 18 Fish tank ★★★
Here is a graph of a tank water level in inches. Tell when the level falls, stays flat and rises, give the lowest level, and the average rate of change from 0 to 6 minutes and from 10 to 16 minutes.
Problem 19 Cupcake profit ★★★
The profit in hundreds of dollars from selling x hundred cupcakes is P(x) = −2x2 + 24x − 40. Use the graph to find the zeros, the maximum, the y-intercept and the interval where the profit is positive, then interpret them.
Problem 20 Compare two functions ★★★
Function f is graphed. Function g(x) = −x2 + 4x + 8. Which has the larger maximum value? Which is positive over the wider interval? (Use √12 ≈ 3.46.)
