Asymptote y = -2, through (0, -1)

Graph y = (1/2)^x - 3

Asymptote y = -3, through (0, -2) and (-1, -1)

Graph y = log_3(x + 1) - 2

Asymptote x = -1, through (0, -2)

Graph y = -(1/3)^x + 2

Asymptote y = 2, through (0, 1) and (-1, -1)

Graph y = 2^(x + 2) + 3

Asymptote y = 3, through (-2, 4)

Graph y = 2(1/2)^x + 2

Asymptote y = 2, through (0, 4) and (-1, 6)

Graph y = log_2(x - 1) + 2

Asymptote x = 1, through (2, 2)

Graph y = 2(1/3)^x - 3

Asymptote y = -3, through (0, -1) and (-1, 3)

Graph y = 2^(x - 1) - 2

Asymptote y = -2, through (1, -1)

Asymptote y = 3, through (0, 2) and (1, 0)

Graph y = log_3(x - 3) - 2

Asymptote x = 3, through (4, -2)

Graph y = (1/3)^x + 1

Asymptote y = 1, through (0, 2) and (-1, 4)

Asymptote y = 1, through (0, 2)

Graph y = 2× 2^x + 1

Asymptote y = 1, through (0, 3) and (1, 5)

Graph y = 2/3 × 3^x + 2

Asymptote y = 2; through (0, 8/3) and (1, 4)

Graph y = log_1/3(x - 4) - 3

Asymptote x = 4; through (5, -3) and (7, -4); decreasing

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)

Worksheets · Precalculus

Precalculus graphing exponential and logarithmic functions worksheet

Precalculus graphs these as a pair of inverse functions, with e and ln as the main bases. Each shift moves the asymptote, so the domain and range follow from it, and a log graph is the matching exponential reflected over y = x.

Also taught in Algebra 2, 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.



Sigma Prep · sigmaprep.io/worksheets Name Graphing Exponential and Log Functions Date Period Graph each function, or write it from its graph or points. Graph $y = 2^{x} - 2$ Write $y = a b^{x}$ through $(0, 3)$ and $(2, 75)$ Graph $y = {(\frac{1}{2})}^{x} - 3$ Graph $y = \log_{3} (x + 1) - 2$ Write $y = a b^{x}$ through $(1, 8)$ and $(3, 32)$ Graph $y = - ⁣ {(\frac{1}{3})}^{x} + 2$ Graph $y = 2^{(x + 2)} + 3$ Write $y = a b^{x}$ through $(0, 4)$ and $(2, 100)$ Graph $y = 2 ⁣ {(\frac{1}{2})}^{x} + 2$ Graph $y = \log_{2} (x - 1) + 2$ Write $y = a b^{x}$ through $(1, 4)$ and $(3, 64)$ Graph $y = 2 ⁣ {(\frac{1}{3})}^{x} - 3$ Graph $y = 2^{(x - 1)} - 2$ Write $y = a b^{x}$ through $(1, 15)$ and $(3, 135)$ Graph $y = - 3^{x} + 3$ Graph $y = \log_{3} (x - 3) - 2$ Write $y = a b^{x}$ through $(1, 8)$ and $(3, 128)$ Graph $y = {(\frac{1}{3})}^{x} + 1$ Graph $y = 2^{x} + 1$ Write $y = a b^{x}$ through $(0, 2)$ and $(2, 8)$ 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.

Graph $y = 2^{x} - 2$
Write $y = a b^{x}$ through $(0, 3)$ and $(2, 75)$
Graph $y = {(\frac{1}{2})}^{x} - 3$
Graph $y = \log_{3} (x + 1) - 2$
Write $y = a b^{x}$ through $(1, 8)$ and $(3, 32)$
Graph $y = - ⁣ {(\frac{1}{3})}^{x} + 2$
Graph $y = 2^{(x + 2)} + 3$
Write $y = a b^{x}$ through $(0, 4)$ and $(2, 100)$
Graph $y = 2 ⁣ {(\frac{1}{2})}^{x} + 2$
Graph $y = \log_{2} (x - 1) + 2$
Write $y = a b^{x}$ through $(1, 4)$ and $(3, 64)$
Graph $y = 2 ⁣ {(\frac{1}{3})}^{x} - 3$
Graph $y = 2^{(x - 1)} - 2$
Write $y = a b^{x}$ through $(1, 15)$ and $(3, 135)$
Graph $y = - 3^{x} + 3$
Graph $y = \log_{3} (x - 3) - 2$
Write $y = a b^{x}$ through $(1, 8)$ and $(3, 128)$
Graph $y = {(\frac{1}{3})}^{x} + 1$
Graph $y = 2^{x} + 1$
Write $y = a b^{x}$ through $(0, 2)$ and $(2, 8)$



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. Graph $y = 2^{x} - 2$ Asymptote $y = - 2$ , through $(0, - 1)$ Write $y = a b^{x}$ through $(0, 3)$ and $(2, 75)$ $y = 3 \cdot 5^{x}$ Graph $y = {(\frac{1}{2})}^{x} - 3$ Asymptote $y = - 3$ , through $(0, - 2)$ and $(- 1, - 1)$ Graph $y = \log_{3} (x + 1) - 2$ Asymptote $x = - 1$ , through $(0, - 2)$ Write $y = a b^{x}$ through $(1, 8)$ and $(3, 32)$ $y = 4 \cdot 2^{x}$ Graph $y = - ⁣ {(\frac{1}{3})}^{x} + 2$ Asymptote $y = 2$ , through $(0, 1)$ and $(- 1, - 1)$ Graph $y = 2^{(x + 2)} + 3$ Asymptote $y = 3$ , through $(- 2, 4)$ Write $y = a b^{x}$ through $(0, 4)$ and $(2, 100)$ $y = 4 \cdot 5^{x}$ Graph $y = 2 ⁣ {(\frac{1}{2})}^{x} + 2$ Asymptote $y = 2$ , through $(0, 4)$ and $(- 1, 6)$ Graph $y = \log_{2} (x - 1) + 2$ Asymptote $x = 1$ , through $(2, 2)$ Write $y = a b^{x}$ through $(1, 4)$ and $(3, 64)$ $y = 4^{x}$ Graph $y = 2 ⁣ {(\frac{1}{3})}^{x} - 3$ Asymptote $y = - 3$ , through $(0, - 1)$ and $(- 1, 3)$ Graph $y = 2^{(x - 1)} - 2$ Asymptote $y = - 2$ , through $(1, - 1)$ Write $y = a b^{x}$ through $(1, 15)$ and $(3, 135)$ $y = 5 \cdot 3^{x}$ Graph $y = - 3^{x} + 3$ Asymptote $y = 3$ , through $(0, 2)$ and $(1, 0)$ Graph $y = \log_{3} (x - 3) - 2$ Asymptote $x = 3$ , through $(4, - 2)$ Write $y = a b^{x}$ through $(1, 8)$ and $(3, 128)$ $y = 2 \cdot 4^{x}$ Graph $y = {(\frac{1}{3})}^{x} + 1$ Asymptote $y = 1$ , through $(0, 2)$ and $(- 1, 4)$ Graph $y = 2^{x} + 1$ Asymptote $y = 1$ , through $(0, 2)$ Write $y = a b^{x}$ through $(0, 2)$ and $(2, 8)$ $y = 2 \cdot 2^{x}$ 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.

Graph $y = 2^{x} - 2$ Asymptote $y = - 2$ , through $(0, - 1)$
Write $y = a b^{x}$ through $(0, 3)$ and $(2, 75)$ $y = 3 \cdot 5^{x}$
Graph $y = {(\frac{1}{2})}^{x} - 3$ Asymptote $y = - 3$ , through $(0, - 2)$ and $(- 1, - 1)$
Graph $y = \log_{3} (x + 1) - 2$ Asymptote $x = - 1$ , through $(0, - 2)$
Write $y = a b^{x}$ through $(1, 8)$ and $(3, 32)$ $y = 4 \cdot 2^{x}$
Graph $y = - ⁣ {(\frac{1}{3})}^{x} + 2$ Asymptote $y = 2$ , through $(0, 1)$ and $(- 1, - 1)$
Graph $y = 2^{(x + 2)} + 3$ Asymptote $y = 3$ , through $(- 2, 4)$
Write $y = a b^{x}$ through $(0, 4)$ and $(2, 100)$ $y = 4 \cdot 5^{x}$
Graph $y = 2 ⁣ {(\frac{1}{2})}^{x} + 2$ Asymptote $y = 2$ , through $(0, 4)$ and $(- 1, 6)$
Graph $y = \log_{2} (x - 1) + 2$ Asymptote $x = 1$ , through $(2, 2)$
Write $y = a b^{x}$ through $(1, 4)$ and $(3, 64)$ $y = 4^{x}$
Graph $y = 2 ⁣ {(\frac{1}{3})}^{x} - 3$ Asymptote $y = - 3$ , through $(0, - 1)$ and $(- 1, 3)$
Graph $y = 2^{(x - 1)} - 2$ Asymptote $y = - 2$ , through $(1, - 1)$
Write $y = a b^{x}$ through $(1, 15)$ and $(3, 135)$ $y = 5 \cdot 3^{x}$
Graph $y = - 3^{x} + 3$ Asymptote $y = 3$ , through $(0, 2)$ and $(1, 0)$
Graph $y = \log_{3} (x - 3) - 2$ Asymptote $x = 3$ , through $(4, - 2)$
Write $y = a b^{x}$ through $(1, 8)$ and $(3, 128)$ $y = 2 \cdot 4^{x}$
Graph $y = {(\frac{1}{3})}^{x} + 1$ Asymptote $y = 1$ , through $(0, 2)$ and $(- 1, 4)$
Graph $y = 2^{x} + 1$ Asymptote $y = 1$ , through $(0, 2)$
Write $y = a b^{x}$ through $(0, 2)$ and $(2, 8)$ $y = 2 \cdot 2^{x}$

How to do these

Graph $y = \ln (x - 2) + 1$ and give its domain

The parent y = ln x has its asymptote at x = 0 and passes through (1, 0).
x - 2 moves everything right 2, so the asymptote is x = 2.
The + 1 moves (1, 0) to (3, 1).

The answer is Asymptote $x = 2$ , through $(3, 1)$ , domain $(2, \infty)$ .

Where students go wrong

Writing the domain of y = ln(x - 2) as x > -2. The input of a log must be positive, so solve x - 2 > 0, which gives x > 2.

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

What you can put on this worksheet

An exponential or a logarithm: Graph $y = 3^{x} + 1$ → Asymptote $y = 1$ , through $(0, 2)$
Write y = ab^x from two points or a graph: Write the equation $y = a b^{x}$ of the graph → $y = 2 \cdot 4^{x}$
Decay, stretches and reflections: Graph $y = 2 \cdot 2^{x} + 1$ → Asymptote $y = 1$ , through $(0, 3)$ and $(1, 5)$
Both shifts, a coefficient inside the log: Graph and give the asymptote: $y = \log_{3} (4 x - 6) + 2$ → Asymptote:
$x = \frac{3}{2}$
A fraction in front: Graph $y = \frac{2}{3} \cdot 3^{x} + 2$ → Asymptote $y = 2$ ; through $(0, \frac{8}{3})$ and $(1, 4)$
Equation from a graph with a shifted asymptote: Write the equation $y = a \cdot b^{x} + k$ of the exponential graphed. → $y = 2^{x} + 1$
A fraction base: decreasing: Graph $y = \log_{\frac{1}{3}} (x - 4) - 3$ → 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.

Precalculus is usually taken around 11th or 12th 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, both shifts, a coefficient inside the log, 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.

Precalculus graphing exponential and logarithmic functions worksheet

Select your difficulty

Graphing Exponential and Log Functions

Graphing Exponential and Log FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these graphing exponential and logarithmic functions worksheets free?+

Do the graphing exponential and logarithmic functions worksheets come with an answer key?+

Are these graphing exponential and logarithmic functions worksheets printable?+

What grade are these graphing exponential and logarithmic functions worksheets for?+

Can I get a different version of the same graphing exponential and logarithmic functions worksheet?+

Is this a free alternative to Kuta Software for graphing exponential and logarithmic functions?+

Can I choose how hard the graphing exponential and logarithmic functions questions are?+

What kinds of question are on a graphing exponential and logarithmic functions worksheet?+

What do students get wrong with graphing exponential and logarithmic functions?+