Question

Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated

Answer 1

See

x is decreased by 3 .

and y is increased by 5

So translation is

• f(x)=(1/4)^x

Hence

• f(x)=(1/4)^x-3+5

So

x will go 3 units right

y will go 5units up

Graph attached

Answer 2

Translations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:

`f(x)=\left((1)/(4)\right)^x`

Translated 3 units to the right:

`f(x-3)=\left((1)/(4)\right)^(x-3)`

Translated 5 units up:

`f(x-3)+5=\left((1)/(4)\right)^(x-3)+5`

`\implies g(x)=f(x-3)+5`

Therefore:

`\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)`