List the asymptote, the domain and the x-intercept of the graph of y = log_3(x - 5) - 1.

x = 5, domain x > 5, x-intercept (8, 0)

The graph of f(x) = log_5(x + 2) has a vertical asymptote. Find it, and give the domain and the x-intercept.

x = -2, domain x > -2, x-intercept (-1, 0)

y = log_3(x - 4) - 2. What are the asymptote, the domain and the x-intercept?

x = 4, domain x > 4, x-intercept (13, 0)

Find the asymptote, the domain and the x-intercept of f(x) = log_10(x + 3).

x = -3, domain x > -3, x-intercept (-2, 0)

State the asymptote, the domain and the x-intercept for the function y = log_10(x - 6) - 2.

x = 6, domain x > 6, x-intercept (106, 0)

For f(x) = log_5(x + 4) - 1, give the asymptote, the domain and the x-intercept.

x = -4, domain x > -4, x-intercept (1, 0)

The graph of y = log_4(x + 1) - 2 has a vertical asymptote. Find it, and give the domain and the x-intercept.

x = -1, domain x > -1, x-intercept (15, 0)

For y = 2(0.8)^x - 5, state the domain, the range, and whether it shows growth or decay.

domain all real numbers; range y > -5; decay

For y = -3^x - 3, state the domain and the range.

domain all real numbers; range y < -3

For y = 5(1/2)^x - 1, state the domain, the range, and whether it shows growth or decay.

domain all real numbers; range y > -1; decay

For y = (0.8)^x - 4, state the domain, the range, and whether it shows growth or decay.

domain all real numbers; range y > -4; decay

For y = -(1/2)^x + 5, state the domain and the range.

domain all real numbers; range y < 5

For y = -(1.5)^x - 6, state the domain and the range.

domain all real numbers; range y < -6

For y = 2(1.5)^x + 1, state the domain, the range, and whether it shows growth or decay.

domain all real numbers; range y > 1; growth

Worksheets · Algebra 2

Features of exponential and logarithmic functions worksheet for Algebra 2

An exponential y = a·bˣ + k levels off at y = k and crosses the y-axis at a + k. A logarithm y = log_b(x − h) + k has a wall at x = h, lives to the right of it, and crosses the x-axis where the log is zero. None of this needs a graph; it is all in the equation.

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.



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Log Features Date Period Answer each question. Find the $y$ -intercept and asymptote Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$ Find the $y$ -intercept and the asymptote of $y = 2 \cdot {(\frac{1}{2})}^{x} - 1$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{4})}^{x} + 3$ Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} - 3$ Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} + 2$ Find the $y$ -intercept and the asymptote of $y = 3^{x} - 1$ Find features of a logarithmic function List the asymptote, the domain and the $x$ -intercept of the graph of $y = \log_{3} (x - 5) - 1$ . The graph of $f (x) = \log_{5} (x + 2)$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. $y = \log_{3} (x - 4) - 2$ . What are the asymptote, the domain and the $x$ -intercept? Find the asymptote, the domain and the $x$ -intercept of $f (x) = \log_{10} (x + 3)$ . State the asymptote, the domain and the $x$ -intercept for the function $y = \log_{10} (x - 6) - 2$ . For $f (x) = \log_{5} (x + 4) - 1$ , give the asymptote, the domain and the $x$ -intercept. The graph of $y = \log_{4} (x + 1) - 2$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. Describe exponential functions For $y = 2 {(0.8)}^{x} - 5$ , state the domain, the range, and whether it shows growth or decay. For $y = - 3^{x} - 3$ , state the domain and the range. For $y = 5 ⁣ {(\frac{1}{2})}^{x} - 1$ , state the domain, the range, and whether it shows growth or decay. For $y = {(0.8)}^{x} - 4$ , state the domain, the range, and whether it shows growth or decay. For $y = - ⁣ {(\frac{1}{2})}^{x} + 5$ , state the domain and the range. For $y = - {(1.5)}^{x} - 6$ , state the domain and the range. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential and Log Features

Date Period

Answer each question.

Find the $y$ -intercept and asymptote
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$
Find the $y$ -intercept and the asymptote of $y = 2 \cdot {(\frac{1}{2})}^{x} - 1$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{4})}^{x} + 3$
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} - 3$
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} + 2$
Find the $y$ -intercept and the asymptote of $y = 3^{x} - 1$

Find features of a logarithmic function
List the asymptote, the domain and the $x$ -intercept of the graph of $y = \log_{3} (x - 5) - 1$ .
The graph of $f (x) = \log_{5} (x + 2)$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept.
$y = \log_{3} (x - 4) - 2$ . What are the asymptote, the domain and the $x$ -intercept?
Find the asymptote, the domain and the $x$ -intercept of $f (x) = \log_{10} (x + 3)$ .
State the asymptote, the domain and the $x$ -intercept for the function $y = \log_{10} (x - 6) - 2$ .
For $f (x) = \log_{5} (x + 4) - 1$ , give the asymptote, the domain and the $x$ -intercept.
The graph of $y = \log_{4} (x + 1) - 2$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept.

Describe exponential functions
For $y = 2 {(0.8)}^{x} - 5$ , state the domain, the range, and whether it shows growth or decay.
For $y = - 3^{x} - 3$ , state the domain and the range.
For $y = 5 ⁣ {(\frac{1}{2})}^{x} - 1$ , state the domain, the range, and whether it shows growth or decay.
For $y = {(0.8)}^{x} - 4$ , state the domain, the range, and whether it shows growth or decay.
For $y = - ⁣ {(\frac{1}{2})}^{x} + 5$ , state the domain and the range.
For $y = - {(1.5)}^{x} - 6$ , state the domain and the range.



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Log FeaturesAnswer keyVersion 1 Date Period Answer each question. Find the $y$ -intercept and asymptote Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$ $(0, 11)$ , $y = 6$ Find the $y$ -intercept and the asymptote of $y = 2 \cdot {(\frac{1}{2})}^{x} - 1$ $(0, 1)$ , $y = - 1$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ $(0, - 1)$ , $y = - 6$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{4})}^{x} + 3$ $(0, 11)$ , $y = 3$ Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} - 3$ $(0, - 2)$ , $y = - 3$ Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} + 2$ $(0, 3)$ , $y = 2$ Find the $y$ -intercept and the asymptote of $y = 3^{x} - 1$ $(0, 0)$ , $y = - 1$ Find features of a logarithmic function List the asymptote, the domain and the $x$ -intercept of the graph of $y = \log_{3} (x - 5) - 1$ . $x = 5$ , domain $x > 5$ , $x$ -intercept $(8, 0)$ The graph of $f (x) = \log_{5} (x + 2)$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. $x = - 2$ , domain $x > - 2$ , $x$ -intercept $(- 1, 0)$ $y = \log_{3} (x - 4) - 2$ . What are the asymptote, the domain and the $x$ -intercept? $x = 4$ , domain $x > 4$ , $x$ -intercept $(13, 0)$ Find the asymptote, the domain and the $x$ -intercept of $f (x) = \log_{10} (x + 3)$ . $x = - 3$ , domain $x > - 3$ , $x$ -intercept $(- 2, 0)$ State the asymptote, the domain and the $x$ -intercept for the function $y = \log_{10} (x - 6) - 2$ . $x = 6$ , domain $x > 6$ , $x$ -intercept $(106, 0)$ For $f (x) = \log_{5} (x + 4) - 1$ , give the asymptote, the domain and the $x$ -intercept. $x = - 4$ , domain $x > - 4$ , $x$ -intercept $(1, 0)$ The graph of $y = \log_{4} (x + 1) - 2$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. $x = - 1$ , domain $x > - 1$ , $x$ -intercept $(15, 0)$ Describe exponential functions For $y = 2 {(0.8)}^{x} - 5$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 5$ ; decay For $y = - 3^{x} - 3$ , state the domain and the range.domain all real numbers; range $y < - 3$ For $y = 5 ⁣ {(\frac{1}{2})}^{x} - 1$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 1$ ; decay For $y = {(0.8)}^{x} - 4$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 4$ ; decay For $y = - ⁣ {(\frac{1}{2})}^{x} + 5$ , state the domain and the range.domain all real numbers; range $y < 5$ For $y = - {(1.5)}^{x} - 6$ , state the domain and the range.domain all real numbers; range $y < - 6$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential and Log FeaturesAnswer keyVersion 1

Date Period

Answer each question.

Find the $y$ -intercept and asymptote
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$ $(0, 11)$ , $y = 6$
Find the $y$ -intercept and the asymptote of $y = 2 \cdot {(\frac{1}{2})}^{x} - 1$ $(0, 1)$ , $y = - 1$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ $(0, - 1)$ , $y = - 6$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{4})}^{x} + 3$ $(0, 11)$ , $y = 3$
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} - 3$ $(0, - 2)$ , $y = - 3$
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{2})}^{x} + 2$ $(0, 3)$ , $y = 2$
Find the $y$ -intercept and the asymptote of $y = 3^{x} - 1$ $(0, 0)$ , $y = - 1$

Find features of a logarithmic function
List the asymptote, the domain and the $x$ -intercept of the graph of $y = \log_{3} (x - 5) - 1$ . $x = 5$ , domain $x > 5$ , $x$ -intercept $(8, 0)$
The graph of $f (x) = \log_{5} (x + 2)$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. $x = - 2$ , domain $x > - 2$ , $x$ -intercept $(- 1, 0)$
$y = \log_{3} (x - 4) - 2$ . What are the asymptote, the domain and the $x$ -intercept? $x = 4$ , domain $x > 4$ , $x$ -intercept $(13, 0)$
Find the asymptote, the domain and the $x$ -intercept of $f (x) = \log_{10} (x + 3)$ . $x = - 3$ , domain $x > - 3$ , $x$ -intercept $(- 2, 0)$
State the asymptote, the domain and the $x$ -intercept for the function $y = \log_{10} (x - 6) - 2$ . $x = 6$ , domain $x > 6$ , $x$ -intercept $(106, 0)$
For $f (x) = \log_{5} (x + 4) - 1$ , give the asymptote, the domain and the $x$ -intercept. $x = - 4$ , domain $x > - 4$ , $x$ -intercept $(1, 0)$
The graph of $y = \log_{4} (x + 1) - 2$ has a vertical asymptote. Find it, and give the domain and the $x$ -intercept. $x = - 1$ , domain $x > - 1$ , $x$ -intercept $(15, 0)$

Describe exponential functions
For $y = 2 {(0.8)}^{x} - 5$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 5$ ; decay
For $y = - 3^{x} - 3$ , state the domain and the range.domain all real numbers; range $y < - 3$
For $y = 5 ⁣ {(\frac{1}{2})}^{x} - 1$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 1$ ; decay
For $y = {(0.8)}^{x} - 4$ , state the domain, the range, and whether it shows growth or decay.domain all real numbers; range $y > - 4$ ; decay
For $y = - ⁣ {(\frac{1}{2})}^{x} + 5$ , state the domain and the range.domain all real numbers; range $y < 5$
For $y = - {(1.5)}^{x} - 6$ , state the domain and the range.domain all real numbers; range $y < - 6$

How to do these

Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 3) - 1$

The log is undefined at x = 3, so that is the asymptote and the domain is x > 3.
y = 0 when log₂(x − 3) = 1, so x − 3 = 2 and x = 5.

The answer is $x = 3$ , domain $x > 3$ , $x$ -intercept $(5, 0)$ .

Where students go wrong

Putting the log asymptote at x = 0 whatever the shift. It sits wherever the inside of the log becomes zero.

Also called asymptotes of exponential functions, domain of a logarithm, intercepts of exponential and log graphs or end behavior of exponentials.

What you can put on this worksheet

The y-intercept and the asymptote: Find the $y$ -intercept and the asymptote of $y = 3 \cdot 4^{x}$ → $(0, 3)$ , $y = 0$
Asymptote and domain of a logarithm: $y = \log_{4} (x - 1)$ . What are the asymptote and the domain? → $x = 1$ , domain $x > 1$
Domain, range, growth or decay: For $y = 2 {(1.5)}^{x} + 1$ , state the domain, the range, and whether it shows growth or decay. → domain all real numbers; range $y > 1$ ; growth

Questions about these worksheets

Yes. Every features of 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 features of 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 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 3: the y-intercept and the asymptote, asymptote and domain of a logarithm and domain, range, growth or decay. Tick as many as you want and set how many of each, or let it spread them evenly.

Putting the log asymptote at x = 0 whatever the shift. It sits wherever the inside of the log becomes zero.

Features of exponential and logarithmic functions worksheet for Algebra 2

Select your difficulty

Find the yyy-intercept and asymptote

Find features of a logarithmic function

Describe exponential functions

Find the yyy-intercept and asymptote

Find features of a logarithmic function

Describe exponential functions

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these features of exponential and logarithmic functions worksheets free?+

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

Are these features of exponential and logarithmic functions worksheets printable?+

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

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

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

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

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

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

Find the $y$ -intercept and asymptote

Find the $y$ -intercept and asymptote