Worksheets · Algebra 2

Graphing exponential and logarithmic functions worksheet for Algebra 2

An exponential flattens against a flat line and a logarithm flattens against an upright one, because each is the other read backwards. Draw the asymptote, mark the one point the curve is pinned to, and the shape follows.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

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

Graphing Exponential and Log Functions

Date Period

Graph each function, or write it from its graph or points.

  1. Graph an exponential or logarithm

    Graph y=2x+3−10−10−5−5551010
  2. Graph y=log⁡2(x+3)+1−10−10−5−5551010
  3. Graph y=3x−3−10−10−5−5551010
  4. Graph y=2(x−3)−2−10−10−5−5551010
  5. Graph y=2x+1−10−10−5−5551010
  6. Graph y=log⁡2(x+2)−2−10−10−5−5551010
  7. Graph y=3x−1−10−10−5−5551010

  1. Write y=abxy = ab^x from points or a graph

    Write y=abx through (1,9) and (−1,1).
  2. Write the equation y=abx of the graph.−10−10−5−5551010
  3. Use (0,1) and (3,27) to find a and b in y=abx, then write the function.
  4. The graph is y=abx. Use the marked points to write its equation.−10−10−5−5551010
  5. Find a and b so that y=abx contains (1,8) and (4,64). Write the equation.
  6. The graph is y=abx. Use the marked points to write its equation.−10−10−5−5551010
  7. An exponential function y=abx passes through (2,4) and (0,64). Write its equation.

  1. Graph y=a⋅bx+ky = a \cdot b^x + k

    Graph y=(13)x−4−10−10−5−5551010
  2. Graph y=−2x+3−10−10−5−5551010
  3. Graph y=2⋅3x−3−10−10−5−5551010
  4. Graph y=2 ⁣(12)x+2−10−10−5−5551010
  5. Graph y=2 ⁣(12)x−3−10−10−5−5551010
  6. Graph y=(12)x+1−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Exponential and Log FunctionsAnswer keyVersion 1

Date Period

Graph each function, or write it from its graph or points.

  1. Graph an exponential or logarithm

    Graph y=2x+3−10−10−5−5551010Asymptote y=3, through (0,4)
  2. Graph y=log⁡2(x+3)+1−10−10−5−5551010Asymptote x=−3, through (−2,1)
  3. Graph y=3x−3−10−10−5−5551010Asymptote y=−3, through (0,−2)
  4. Graph y=2(x−3)−2−10−10−5−5551010Asymptote y=−2, through (3,−1)
  5. Graph y=2x+1−10−10−5−5551010Asymptote y=1, through (0,2)
  6. Graph y=log⁡2(x+2)−2−10−10−5−5551010Asymptote x=−2, through (−1,−2)
  7. Graph y=3x−1−10−5510−10−5510Asymptote y=−1, through (0,0)

  1. Write y=abxy = ab^x from points or a graph

    Write y=abx through (1,9) and (−1,1).y=3⋅3x
  2. Write the equation y=abx of the graph.−10−10−5−5551010y=6 ⁣(12)x
  3. Use (0,1) and (3,27) to find a and b in y=abx, then write the function.y=3x
  4. The graph is y=abx. Use the marked points to write its equation.−10−10−5−5551010y=9 ⁣(13)x
  5. Find a and b so that y=abx contains (1,8) and (4,64). Write the equation.y=4⋅2x
  6. The graph is y=abx. Use the marked points to write its equation.−10−10−5−5551010y=8 ⁣(12)x
  7. An exponential function y=abx passes through (2,4) and (0,64). Write its equation.y=64 ⁣(14)x

  1. Graph y=a⋅bx+ky = a \cdot b^x + k

    Graph y=(13)x−4−10−10−5−5551010Asymptote y=−4, through (0,−3) and (−1,−1)
  2. Graph y=−2x+3−10−10−5−5551010Asymptote y=3, through (0,2) and (1,1)
  3. Graph y=2⋅3x−3−10−10−5−5551010Asymptote y=−3, through (0,−1) and (1,3)
  4. Graph y=2 ⁣(12)x+2−10−10−5−5510105Asymptote y=2, through (0,4) and (−1,6)
  5. Graph y=2 ⁣(12)x−3−10−10−5−5551010Asymptote y=−3, through (0,−1) and (−1,1)
  6. Graph y=(12)x+1−10−10−5−5551010Asymptote y=1, through (0,2) and (−1,3)

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

How to do these

Graph y=2x+1

  1. Far to the left the power fades to nothing, so y settles at 1.
  2. At x = 0 the power is 1, so the curve passes through (0, 2).
  3. To the right it doubles every step and climbs away.

The answer is Asymptote y=1, through (0,2).

Where students go wrong

Letting the curve touch its asymptote. It gets closer forever and never arrives. The other slip is reading a log as defined everywhere: it stops dead at its upright asymptote and has nothing to the left of it.

Also called exponential graphs, logarithm graphs or plotting growth and decay.

What you can put on this worksheet

An exponential or a logarithm
Graph y=3x+1 → Asymptote y=1, through (0,2)
Write y = ab^x from two points or a graph
The graph is y=abx. Use the marked points to write its equation. → y=3⋅3x
Decay, stretches and reflections
Graph y=2⋅2x+1 → Asymptote y=1, through (0,3) and (1,5)
Graph with shifts and a stretch
Graph and give the asymptote: y=log⁡3(4x−6)+2 → Asymptote:
x=32
A fraction in front
Graph y=32⋅3x+2. → Asymptote y=2; through (0,72) and (1,132)
Equation from a graph with a shifted asymptote
Use the asymptote and the two marked points to find the equation y=a⋅bx+k. → y=−2x−3
A fraction base: decreasing
Graph y=log⁡13(x−4)−3 → Asymptote x=4; through (5,−3) and (7,−4); decreasing
Graph, with domain and range
Graph y=log⁡3(x+4)−4 and give its domain and range. → Domain x>−4; range all real numbers;
asymptote x=−4; through (−3,−4) and (−1,−3)

Questions about these worksheets

Yes. Every graphing exponential and logarithmic 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 2 is usually taken around 10th or 11th 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 graphing exponential and logarithmic 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 two 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 8: an exponential or a logarithm, write y = ab^x from two points or a graph, decay, stretches and reflections, graph with shifts and a stretch, a fraction in front, equation from a graph with a shifted asymptote, a fraction base: decreasing and graph, with domain and range. Tick as many as you want and set how many of each, or let it spread them evenly.

Letting the curve touch its asymptote. It gets closer forever and never arrives. The other slip is reading a log as defined everywhere: it stops dead at its upright asymptote and has nothing to the left of it.