Question

Question #faf22

Answer 1

The given function is linear, and it can also be expressed as
`f(x) = -2x +8` in the form `f(x) = ax + b`.

Explanation:

The given function is linear because the starting value is being added and the common difference is being multiplied.

There are two functions; linear and exponential. A linear function is one that has a common difference (which means it is being added or subtracted), and on a graph it will be a straight line.

An exponential function, however, is one that has a common ratio (which means it is being multiplied), and on a graph it will be a curved line.

The function notation for a linear equation is

`f(x) = ax + b`

while the exponential equation would be

`f(x) = a^x*b`

In this problem, the starting value, `f(0)`, or `y`-intercept (which are all the same thing) is `8`, and the common difference is `-2`. As you can see, the starting value is being added and the common difference is being multiplied, so therefore the equation is linear.

It is technically already in the form `f(x) = ax + b`, unless if you want to change the order to have the common difference first and then the starting value.