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

Answer:

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

Step-by-step 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

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