Question

Describe the graphs of the functions f(x) = 2x + 1 and g(x) = -2x + 1. Compare and contrast the domain and range of f(x) and g(x).

Answer 1

@SolomonZelman

Answer 2

\(\color{#000000 }{ \displaystyle f(x) }\) and \(\color{#000000 }{ \displaystyle -f(x) }\)
are reflections of each other across the x-axis.

Answer 3

Therefore, \(\color{#000000 }{ \displaystyle f(x)=2x }\)
\(\color{#000000 }{ \displaystyle g(x)=-2x }\)

Are reflections of each other across the x-axis.

Answer 4

And so would be \(\color{#000000 }{ \displaystyle f(x)=2x+1 }\)
\(\color{#000000 }{ \displaystyle g(x)=-2x-1 }\)

reflections of each other across the x-axis.

Answer 5

\(\color{#000000 }{ \displaystyle g(x)=-2x+1=(-2x-1)+2 }\)

Answer 6

So you can tell that \(\color{#000000 }{ \displaystyle g(x) }\) is a reflection
across the x-axis of the \(\color{#000000 }{ \displaystyle f(x) }\), and then
\(\color{#000000 }{ \displaystyle g(x) }\) is shifted by .... (you should tell me this)

Answer 7

f(x)?

Answer 8

@SolomonZelman