Question

F(7)=
g(7)=
The equation for f(x) is
The equation for g(x) is

Answer 1

Answer: f(7) = -128

g(7) = 26

Equation of f(x): f(x)= -11x-51

Equation of g(x): g(x)=3x+5

Explanation:

Rate of change of a function:
`(f(x_2)-f(x_1))/(x_2-x_1)`

From the table. Rate of change in f(x)=
`(f(1)-f(0))/(1-0)=(-62+51)/(1)=-11`

Rate of change in g(x)=
`(g(1)-g(0))/(1-0)=(8-5)/(1)=3`

Also, the rate of change throughout the function is the same, hence both are linear functions.

Equation of linear function:
`f(x)=mx+c`, where m= rate of change of function, c = f(x) at x=0.

From table, f(0)= -51 , g(0)=5

Equation of f(x): f(x)= -11x-51

Equation of g(x): g(x)=3x+5

f(7) = -11(7)-51 = -77-51 = -128

g(7) = 3(7)+5 = 21+5 = 26

f(7) = -128

g(7) = 26