# Comparing Linear and Exponential Functions Worksheets

We look at the different uses of these types of functions. It really depends on the nature of what you are attempting to model. Linear functions can be used to model very consistent situations where the change is always occurring, and we just need to get the math to go with it. In situation where something scales up or down in slow and then explosive manner, exponential functions are your math of choice. Below you will find a great collection of worksheets and lessons that teaches you how to compare linear and exponential forms of functions. We will also include the concept of quadratic functions.

### Aligned Standard: HSF-LE.A.1a

- Interpret the Graphed Function Step-by-step Lesson - You will learn to identify linear, exponential, and quadratic functions by the shape trend of their graphs.
- Guided Lesson - In addition to interpreting graphs, you will need to make them here first.
- Guided Lesson Explanation - We teach you a step beyond graphing and understanding the differences in tables.
- Practice Worksheet - This is quite a long one to print out, but well worth it.
- Matching Worksheet - I got a little selfish here. I always had students have difficulty with these two graphing forms, so I focused on those.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We give you a function. You tell us if it is in linear, quadratic, or exponential form.

- Homework 1 - You can compare successive y-values to determine which type of function the table describes.
- Homework 2 - The graph of a quadratic function is a parabola that opens up or down. The given graph does not approach a parabola that opens downwards, so it is not quadratic.
- Homework 3 - Since the first differences are same, the function is linear.

### Practice Worksheets

Determine the format based on a table and a graph.

- Practice 1 - Is this function linear, quadratic, or exponential?
- Practice 2 - What type of function does this graph show?
- Practice 3 - Don't let the straight line confuse you.

### Math Skill Quizzes

Once again the goal is to determine the format.

- Quiz 1 - If the ratios of multiple are same, the function is exponential.
- Quiz 2 - The graph of an exponential function has one horizontal asymptote. The given graph does not approach a horizontal asymptote, so it is not exponential.
- Quiz 3 - It is up to you to find the first differences in table.

### How to Compare Linear and Exponential Functions

Linear functions represent straight lines that can be plotted within the coordinate plane. They are used to model a relationship where two quantities have a direct connection. As one increases, so does the other and vice versa. Exponential functions contain an exponent somewhere within it, but it generally positioned to the right of the equal sign. Unlike its linear counterpart, exponential forms model a system that is a constant state of flux where the independent variable exhibits a proportional change. So, they both model change, but linear is slowly and steady and exponential is slow and then explosive. As a result these functions are used to model different types of things based on the degree and rate of change that is displayed by your individual scenario.

Both linear and exponential functions are the types of functions that considers the power of independent variables. In other words, a linear function has the highest power 1 in its equation, i.e., y = mx + c. Regardless of the values of m and c, on a graph, the result will always be a straight line. By definition, m is the slope of the line, while c is the y-intercept of the function y. On the other hand, an exponential function is the one where the power is non-trivial (not 0 or 1). The equation is usually written in the form of y=ax^{n}, where n is the non-trivial power. Here, a is the y-intercept of function y, while n is the base of the function.

**Linear** - They follow the form of f(x) = ax + b. (a is the slope and b is the y-intercept)

** Exponential** - They follow the form of f(x) = ab^{x}. (a is the scaling factor {constant}, b is the base)