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.

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Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Comparing Functions

Date Period

Answer each question.

  1. Compare two functions

    Function A: y=−3 when x=0, and y goes down by 3 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x3579y14223038
  2. Function A: y=−x+4Function B is the line graphed below.Which function has the greater y-intercept?−10−10−5−5551010
  3. Function A: y=−x−6Function B is the line graphed below.Which function changes faster (has the greater absolute rate of change)?−10−5551010−10−5
  4. Function A: y=2 when x=0, and y goes down by 1 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x1357y−2−6−10−14
  5. Function A: y=2x+6Function B is shown in the table.Which function has the greater y-intercept?x3579y5132129
  6. Function A: y=−7 when x=0, and y goes down by 3 each time x increases by 1.Function B is the line graphed below.Which function has the greater y-intercept?−10−5−5551010−10
  7. Function A: y=x−5Function B is the line graphed below.Which function has the greater slope?−10−10−5−5510105
  8. Function A: y=−6 when x=0, and y goes up by 3 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x−7−5−3−1y−20−16−12−8
  9. Function A: y=−4xFunction B is shown in the table.Which function changes faster (has the greater absolute rate of change)?x−7−5−3−1y−20−14−8−2
  10. Function A: y=−4 when x=0, and y goes up by 2 each time x increases by 1.Function B is shown in the table.Which function has the greater y-intercept?x3579y4101622

  1. Decide if the function is linear

    Is the function linear or nonlinear?x−1012y−3−6−9−12
  2. Is the function linear or nonlinear?x−1135y22−6−22
  3. Is the function linear or nonlinear? y=x8+3
  4. Is the function linear or nonlinear?x−2−101y−13−9−5−1
  5. Is the function linear or nonlinear? xy=4
  6. Is the function linear or nonlinear?x0123y−6−4212
  7. Is the function linear or nonlinear? y=−x−6
  8. Is the function linear or nonlinear? y=2x
  9. Is the function linear or nonlinear? 4x+3y=20
  10. Is the function linear or nonlinear?x0123y2−3−8−13

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. Compare two functions

    Function A: y=−3 when x=0, and y goes down by 3 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x3579y14223038Function B: 4>−3
  2. Function A: y=−x+4Function B is the line graphed below.Which function has the greater y-intercept?−10−10−5−5551010Function A: 4>−3
  3. Function A: y=−x−6Function B is the line graphed below.Which function changes faster (has the greater absolute rate of change)?−10−5551010−10−5Function B: ∣3∣>∣−1∣
  4. Function A: y=2 when x=0, and y goes down by 1 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x1357y−2−6−10−14Function A: −1>−2
  5. Function A: y=2x+6Function B is shown in the table.Which function has the greater y-intercept?x3579y5132129Function A: 6>−7
  6. Function A: y=−7 when x=0, and y goes down by 3 each time x increases by 1.Function B is the line graphed below.Which function has the greater y-intercept?−10−5−5551010−10Function B: −4>−7
  7. Function A: y=x−5Function B is the line graphed below.Which function has the greater slope?−10−10−5−5510105Function A: 1>−4
  8. Function A: y=−6 when x=0, and y goes up by 3 each time x increases by 1.Function B is shown in the table.Which function has the greater slope?x−7−5−3−1y−20−16−12−8Function A: 3>2
  9. Function A: y=−4xFunction B is shown in the table.Which function changes faster (has the greater absolute rate of change)?x−7−5−3−1y−20−14−8−2Function A: ∣−4∣>∣3∣
  10. Function A: y=−4 when x=0, and y goes up by 2 each time x increases by 1.Function B is shown in the table.Which function has the greater y-intercept?x3579y4101622Function A: −4>−5

  1. Decide if the function is linear

    Is the function linear or nonlinear?x−1012y−3−6−9−12Linear
  2. Is the function linear or nonlinear?x−1135y22−6−22Nonlinear
  3. Is the function linear or nonlinear? y=x8+3Linear
  4. Is the function linear or nonlinear?x−2−101y−13−9−5−1Linear
  5. Is the function linear or nonlinear? xy=4Nonlinear
  6. Is the function linear or nonlinear?x0123y−6−4212Nonlinear
  7. Is the function linear or nonlinear? y=−x−6Linear
  8. Is the function linear or nonlinear? y=2xNonlinear
  9. Is the function linear or nonlinear? 4x+3y=20Linear
  10. Is the function linear or nonlinear?x0123y2−3−8−13Linear

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 function has the greater slope?

  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

Equations, tables, graphs and words
Function A: y=5x+1
Function B is shown in the table.
Which function has the greater y-intercept?
x0123y−4−7−10−13 → Function A: 1>−4
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: equations, tables, graphs and words 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.