Precalculus features of exponential and logarithmic functions worksheet

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.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Log Features Date Period Answer each question. Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{3} (x - 6) - 2$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{5})}^{x} - 3$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5)$ Find the $y$ -intercept and the asymptote of $y = 4 \cdot {(\frac{1}{2})}^{x} - 5$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5) - 1$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 2$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 6)$ Find the $y$ -intercept and the asymptote of $y = 6 \cdot {(\frac{1}{3})}^{x} + 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5)$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot 2^{x} - 5$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5)$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5) - 2$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 5^{x} + 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{10} (x - 5)$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 3^{x} + 4$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5) - 2$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{2})}^{x} + 1$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 6) - 1$ 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 the asymptote of $y = 5 \cdot 2^{x} + 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{3} (x - 6) - 2$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{5})}^{x} - 3$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5)$
Find the $y$ -intercept and the asymptote of $y = 4 \cdot {(\frac{1}{2})}^{x} - 5$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5) - 1$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 2$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 6)$
Find the $y$ -intercept and the asymptote of $y = 6 \cdot {(\frac{1}{3})}^{x} + 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5)$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot 2^{x} - 5$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5)$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5) - 2$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 5^{x} + 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{10} (x - 5)$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 3^{x} + 4$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5) - 2$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{2})}^{x} + 1$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 6) - 1$



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Log FeaturesAnswer keyVersion 1 Date Period Answer each question. Find the $y$ -intercept and the asymptote of $y = 5 \cdot 2^{x} + 6$ $(0, 11)$ , $y = 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{3} (x - 6) - 2$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(15, 0)$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{5})}^{x} - 3$ $(0, 0)$ , $y = - 3$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$ Find the $y$ -intercept and the asymptote of $y = 4 \cdot {(\frac{1}{2})}^{x} - 5$ $(0, - 1)$ , $y = - 5$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5) - 1$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(7, 0)$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 2$ $(0, 3)$ , $y = - 2$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 6)$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(7, 0)$ Find the $y$ -intercept and the asymptote of $y = 6 \cdot {(\frac{1}{3})}^{x} + 6$ $(0, 12)$ , $y = 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot 2^{x} - 5$ $(0, - 2)$ , $y = - 5$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ $(0, - 1)$ , $y = - 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5) - 2$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(21, 0)$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 5^{x} + 6$ $(0, 14)$ , $y = 6$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{10} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 3^{x} + 4$ $(0, 12)$ , $y = 4$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5) - 2$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(30, 0)$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{2})}^{x} + 1$ $(0, 9)$ , $y = 1$ Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 6) - 1$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(11, 0)$ 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 the asymptote of $y = 5 \cdot 2^{x} + 6$ $(0, 11)$ , $y = 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{3} (x - 6) - 2$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(15, 0)$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{5})}^{x} - 3$ $(0, 0)$ , $y = - 3$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$
Find the $y$ -intercept and the asymptote of $y = 4 \cdot {(\frac{1}{2})}^{x} - 5$ $(0, - 1)$ , $y = - 5$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5) - 1$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(7, 0)$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 2$ $(0, 3)$ , $y = - 2$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 6)$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(7, 0)$
Find the $y$ -intercept and the asymptote of $y = 6 \cdot {(\frac{1}{3})}^{x} + 6$ $(0, 12)$ , $y = 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot 2^{x} - 5$ $(0, - 2)$ , $y = - 5$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{2} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot 5^{x} - 6$ $(0, - 1)$ , $y = - 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{4} (x - 5) - 2$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(21, 0)$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 5^{x} + 6$ $(0, 14)$ , $y = 6$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{10} (x - 5)$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(6, 0)$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 3^{x} + 4$ $(0, 12)$ , $y = 4$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 5) - 2$ $x = 5$ , domain $x > 5$ , $x$ -intercept $(30, 0)$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot {(\frac{1}{2})}^{x} + 1$ $(0, 9)$ , $y = 1$
Find the asymptote, the domain and the $x$ -intercept of $y = \log_{5} (x - 6) - 1$ $x = 6$ , domain $x > 6$ , $x$ -intercept $(11, 0)$

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: Find the asymptote and the domain of $y = \log_{4} (x - 1)$ → $x = 1$ , domain $x > 1$

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.

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 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 2: the y-intercept and the asymptote and asymptote and domain of a logarithm. 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.

Precalculus features of exponential and logarithmic functions worksheet

Select your difficulty

Exponential and Log Features

Exponential and Log FeaturesAnswer keyVersion 1

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?+