Question

Katie says the graph of y=8 . (1/2)^x is the same as the graph of f(x)=8 . (1/2)^x. Do you agree? Explain your reasoning.

Answer 1

Yes

Explanation:

Katie's Graph equation:
`y=8((1)/(2))^x`

Another graph equation:
`f(x)=8((1)/(2))^x`

Since the right hand side of both the equations of graphs are equal

So, Left hand side of both equations of graphs must be equal

So, :
`y=f(x)`

So, the graph of
`y=8((1)/(2))^x` is the same as the graph of
`f(x)=8((1)/(2))^x`

Refer the attached figure

Purple line :
`f(x)=8((1)/(2))^x`

Red line :
`y=8((1)/(2))^x`

Answer 2

Yes

Explanation:

Yes, the graph of y=
`8{*}((1)/(2))^(x)` is same as the graph of f(x)=
`8{*}((1)/(2))^(x)` because the right hand side of both the equations is equal that is
`8{*}((1)/(2))^(x)`, therefore by substituting different values of x in both equations, we obtain the same graph.