Question

Create a graph of the combined function h(x) = f(x) / g(x) in which f(x) = x - 6 and g(x) = x + 6. On your graph, show the graphs of f(x) and g(x) also.

Answer 1

we have

f(x)=x-6f(x)=x−6 -----> equation A

This is a linear equation with slope m=1m=1 and a y-intercept equal to -6−6

g(x)=x+6g(x)=x+6 -----> equation B

This is a linear equation with slope m=1m=1 and a y-intercept equal to 66

The function f(x) and g(x) are parallel lines

we know that

h(x)=f(x)+g(x)h(x)=f(x)+g(x)

Substitute

h(x)=x-6+x+6h(x)=x−6+x+6

h(x)=2xh(x)=2x

This is a linear equation with slope m=2m=2 that passes through the origin ( represent a direct variation)

Using a graphing tool

see the attached figure