# Common Core Standards: Math See All Teacher Resources

#### The Standards

# High School: Functions

### Linear, Quadratic, and Exponential Models F-LE.1a

**a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.**

Students have to know the differences between linear functions and exponential functions. In simplest terms, a linear function one that takes the form *y* = *mx* + *b* and an exponential function is one in which *y* = *a*^{x}.

The best way to understand these functions based on distances is to make a table of values and observe how the *y* values change for each increase in *x*. For instance, we can look at *f*(*x*) = 2*x* and *f*(*x*) = 2^{x}.

If we graph the two functions, we'll see the difference between the line and the exponential. (Hint: The line is blue and the exponential is red.)