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

The answer in the attached figure

Explanation:

we have

`f(x)=x-6` -----> equation A

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

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

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

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

we know that

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

Substitute

`h(x)=x-6+x+6`

`h(x)=2x`

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

Using a graphing tool

see the attached figure

Answer 2

The graph of f(x) has a slope of 1/1 and a y intercept of -6. To graph, place a point at (0,_6). Then move up 1 and over 1. This will give another point at (1,-5). Draw a line through the points.

The graph of g(x) has a slope of 1/1 and a y intercept of 6. To graph, place a point at (0,6). Then move up 1 and over 1. This will give another point at (1,7). Draw a line through the points

lines are parallel since slopes are the same.

h(x) = x-6+x+6= 2x or 2x+0. This line has a slope of 2/1 and a y intercept of 0. To graph, place a point at (0,0). Then move up 2 and over 1. This will give another point at (1,2). Draw a line through the points.