Question

Write the equation of the translated parent function f(x) = ex where is it translated 1 unit right and 2 units down

Answer 1

Given the parent function:

$f(x)=e^x$

first, to translate it 1 unit right, we have to find f(x-1):

$f(x-1)=e^{x-1}$

next, to translate it 2 units down, we have to find the following expression:

$\begin{gathered} f(x)+c,c<0 \\ \Rightarrow f(x)+c=e^x-2 \end{gathered}$

combining both transformations, we get:

$g(x)=e^{x-1}-2$

therefore, g(x) = e^(x-1) - 2 is the translation of the parent function 1 unit right and 2 units down