# Question #faf22

Nov 5, 2017

The given function is linear, and it can also be expressed as
$f \left(x\right) = - 2 x + 8$ in the form $f \left(x\right) = a x + b$.

#### 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

$f \left(x\right) = a x + b$

while the exponential equation would be

$f \left(x\right) = {a}^{x} \cdot b$

In this problem, the starting value, $f \left(0\right)$, 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 $f \left(x\right) = a x + b$, unless if you want to change the order to have the common difference first and then the starting value.