Linear functions

Question

For a linear function, if f(0)=-1 and f(1)=1 , find : 

 

a) f(x) = ax+b 

b) f(5) 

c) the value of x when f(x)=15 

Answer 1

Kyle,

 

Since f(0) = −1, −1 is the y-intercept, b. If you then put x = 1 and f(1) = 1 after plugging in b, you can solve for a. You can also find a using the slope formula:

 

m = (1 − (-1))/(1 − 0) = 2.

 

The answer to a) is f(x) = 2x − 1.

 

For b), f(5) = 2(5) − 1 = 9.

 

For c), solve f(x) = 15:

 

2x − 1 = 15

 

2x = 16

 

x = 8.