Question

Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g are shown in the table below. By how much does g exceed f when x = 5?

Answer 1

g(x) exceed f(x) by
`10` when
`x=5`

Explanation:

step 1

Find the equation of function f(x)

we know that

The initial value is the y-intercept of the linear function (value of y when the value of x is equal to zero)

so

`b=17`

The rate of change is equal to the slope

so

`m=-3`

therefore

`f(x)=-3x+17`

step 2

Find the equation of function g(x)

Let

`A(0,-8),B(2,0)`

Find the slope

`m=(0+8)/(2-0)=4`

`b=-8` ----> point A

therefore

`g(x)=4x-8`

step 3

Find the value of f(x) and g(x) for
`x=5`

`f(5)=-3(5)+17=2`

`g(5)=4(5)-8=12`

Find the difference

`g(5)-f(5)=12-2=10`