Worksheets · Algebra 1

Comparing functions worksheet

Two functions can come in different forms: an equation, a table, a graph or words. Put each one in the same terms, its rate of change and its starting value, and the comparison is just two numbers.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Comparing Functions

Date Period

Answer each question.

  1. Function A: y=x. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y−42814
  2. Is the function linear or nonlinear? y=−7x−1
  3. Function A: y=−4x+5. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y31−1−3
  4. Is the function linear or nonlinear? y=x2−9
  5. Function A: y=−x+2. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y8101214
  6. Is the function linear or nonlinear?x0246y5132129
  7. Function A: y=−x+6. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y0−6−12−18
  8. Is the function linear or nonlinear? y=4x
  9. Function A: y=2x−6. Function B is shown in the table.Which has the greater rate of change?x0123y−4−10−16−22
  10. Is the function linear or nonlinear? y=x8+3
  11. Function A: y=6x−8. Function B is shown in the table.Which has the greater rate of change?x0123y8765
  12. Is the function linear or nonlinear? y=x9+3
  13. Function A: y=4x+3. Function B is shown in the table.Which has the greater rate of change?x0123y−3−6−9−12
  14. Is the function linear or nonlinear?x1234y−421226
  15. Function A: y=−x+5. Function B is shown in the table.Which has the greater rate of change?x0123y0−6−12−18
  16. Is the function linear or nonlinear? y=2x
  17. Function A: y=−4x−8. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y15913
  18. Is the function linear or nonlinear?x1234y46810
  19. Function A: y=x−7. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y−8−13−18−23
  20. Is the function linear or nonlinear?x−1012y−5−6−5−2

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Comparing FunctionsAnswer keyVersion 1

Date Period

Answer each question.

  1. Function A: y=x. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y−42814Function A: 0>−4
  2. Is the function linear or nonlinear? y=−7x−1Linear
  3. Function A: y=−4x+5. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y31−1−3Function A: 5>3
  4. Is the function linear or nonlinear? y=x2−9Nonlinear
  5. Function A: y=−x+2. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y8101214Function B: 8>2
  6. Is the function linear or nonlinear?x0246y5132129Linear
  7. Function A: y=−x+6. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y0−6−12−18Function A: 6>0
  8. Is the function linear or nonlinear? y=4xNonlinear
  9. Function A: y=2x−6. Function B is shown in the table.Which has the greater rate of change?x0123y−4−10−16−22Function A: 2>−6
  10. Is the function linear or nonlinear? y=x8+3Linear
  11. Function A: y=6x−8. Function B is shown in the table.Which has the greater rate of change?x0123y8765Function A: 6>−1
  12. Is the function linear or nonlinear? y=x9+3Linear
  13. Function A: y=4x+3. Function B is shown in the table.Which has the greater rate of change?x0123y−3−6−9−12Function A: 4>−3
  14. Is the function linear or nonlinear?x1234y−421226Nonlinear
  15. Function A: y=−x+5. Function B is shown in the table.Which has the greater rate of change?x0123y0−6−12−18Function A: −1>−6
  16. Is the function linear or nonlinear? y=2xNonlinear
  17. Function A: y=−4x−8. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y15913Function B: 1>−8
  18. Is the function linear or nonlinear?x1234y46810Linear
  19. Function A: y=x−7. Function B is shown in the table.Which has the greater initial value (y-intercept)?x0123y−8−13−18−23Function A: −7>−8
  20. Is the function linear or nonlinear?x−1012y−5−6−5−2Nonlinear

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Function A: y=3x+1. Function B is the table (0,2),(1,4),(2,6). Which has the greater rate of change?

  1. Function A changes by 3 for each step in x.
  2. In the table, y goes up 2 each time x goes up 1.
  3. 3 is more than 2.

The answer is Function A: 3>2.

Where students go wrong

Comparing the y-values in the table instead of how fast they change. A table that starts higher can still grow more slowly.

Also called comparing linear functions, linear and nonlinear functions or comparing functions in different forms.

What you can put on this worksheet

An equation against a table
Function A: y=4x+4. Function B is shown in the table.Which has the greater rate of change?x0123y1−2−5−8 → Function A: 4>−3
Linear or nonlinear
Is the function linear or nonlinear?x0246y1−11−47−107 → Nonlinear

Questions about these worksheets

Yes. Every comparing functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the comparing functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: an equation against a table and linear or nonlinear. Tick as many as you want and set how many of each, or let it spread them evenly.

Comparing the y-values in the table instead of how fast they change. A table that starts higher can still grow more slowly.