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

Answer:

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:

$f(x)=\left(\dfrac{1}{4}\right)^x$

Translated 3 units to the right:

$f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}$

Translated 5 units up:

$f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5$

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

Therefore:

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