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?

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calculista calculista · Answer 1 · 2019-02-15T20:51:35+01:00

Answer:

g(x) exceed f(x) by [tex]10[/tex] when [tex]x=5[/tex]

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

[tex]b=17[/tex]

The rate of change is equal to the slope

so

[tex]m=-3[/tex]

therefore

[tex]f(x)=-3x+17[/tex]

step 2

Find the equation of function g(x)

Let

[tex]A(0,-8),B(2,0)[/tex]

Find the slope

[tex]m=(0+8)/(2-0)=4[/tex]

[tex]b=-8[/tex] ----> point A

therefore

[tex]g(x)=4x-8[/tex]

step 3

Find the value of f(x) and g(x) for [tex]x=5[/tex]

[tex]f(5)=-3(5)+17=2[/tex]

[tex]g(5)=4(5)-8=12[/tex]

Find the difference

[tex]g(5)-f(5)=12-2=10[/tex]