Question #faf22

1 Answer
Nov 5, 2017

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

while the exponential equation would be

f(x) = a^x*bf(x)=axb

In this problem, the starting value, f(0)f(0), or yy-intercept (which are all the same thing) is 88, and the common difference is -22. 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 + bf(x)=ax+b, unless if you want to change the order to have the common difference first and then the starting value.