Key Features of Graphs Worksheet with Answers – Algebra 1 (Free PDF)

Problem 1 Intercepts of a line ★★★

Find the x– and y-intercepts of y = 2x − 6.

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:

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:

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.

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:

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.)