Question #faf22

1 Answer
Nov 5, 2017

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.