## Graphing Exponential and Logarithmic Functions

#### Aligned To Common Core Standard:

**High School Interpreting Functions** - HSF-IF.C.7e

How to Graph Exponential and Logarithmic Functions?
Exponential function and Logarithm function are essential aspects in the field of mathematics. Given that on a theoretical basis, both of them are inversely proportional to each other. Here, let us look at the procedure to construct graphs of both these functions and their relativity with each other.
**Exponential Function** - The exponential function is a simpler equation, where the unknown variable is an exponent rather than the base. Let us consider an example of the function, f(x)= 5^{x} and f(x)= 7^{x}. Now, whatever the value of x, it will increase or decrease in terms of 5 and 7. Look at the graph and the values presented below on the function.
x, f(x)= 5^{x}, f(x)= 7^{x} : 0, 1, 1 | 1, 5, 7 | 2, 25, 49 | 3, 125, 343 | 4, 625, 2401 | 5, 3125, 16807
**Logarithmic Function** - By definition, the logarithmic function is an equation that consists of the independent variable which occurs in the form of the logarithm. Close values of the function create asymptotic graphs that approach arbitrarily close to each other. Let us consider an example with the functions f(x)=log_{2} x and f(x)=log_{10} x.
x, f(x)=log_{2}x, f(x)= log_{10} x: 1, 0, 0 | 2, 1, 0.30103 | 3, 1.584963, 0.477121 | 4, 2, 0.60206 | 5, 2.321928, 0.69897 | 6, 2.584963, 0.778151. These lessons and worksheets show students how to graph these two common functions that are the inverse of one another.

### Printable Worksheets And Lessons

- Differential Exponent
Graph Step-by-step Lesson- This graph was a slight challenge
for me when I first came across these problems again.

- Guided Lesson
- You will come across one exponent and two logarithmic.

- Guided Lesson Explanation
- See if these follow the general rules to help it make more sense
for you.

- Practice Worksheet
- By the time students get to number six, they should have a solid
understanding of how to get this all rolling.

- Matching Worksheet
- Match the lettered values to the tables and graphs; that does
make it easier..

#### Homework Sheets

Understanding how negative values affect the graphs are key.

- Homework 1 - Since 4-x is zero when x=4, we will choose x values around 4 in our table of values.
- Homework 2 - We
can graph x= 4
^{y}by using the same method for exponential functions, except this time we will choose values for y and then compute the corresponding values for x. - Homework 3 - Graph f(x) = 6
^{7-x}: At first looks like 6^{x}should reflect across the y-axis since x is negative. However, the graph tells a different story.

#### Practice Worksheets

Time to start understanding the concept of function comparisons. What happens if you change one variable?

- Practice 1 - Rewriting f(x) =y= log
_{11x}in exponential form we get x= 11^{y}. - Practice 2 - Graph f(x) = 4
^{1-x} - Practice 3 - Rewite all the problems first, it will make it faster for you.

#### Math Skill Quizzes

We did pack a lot of questions into these sheets.