Question

the parent function for the graph to the right is of the form $y = ab^x$. write the parent function. then write a function for the translation indicated

translation left 7 units, down 5 units

the parent function for the graph shown is $y = \square$

(simplify your answer. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Identify parent function form

The problem states the parent function is of the form $y=ab^x$. The given graph is an exponential growth curve that passes through $(0,1)$ and $(1,2)$, so $a=1$, $b=2$.
Expression: $y=2^x$

Step2: Apply horizontal translation left

For a left shift of 7 units, replace $x$ with $x+7$.
Expression: $y=2^{x+7}$

Step3: Apply vertical translation down

For a down shift of 5 units, subtract 5 from the function.
Expression: $y=2^{x+7}-5$

Answer:

Parent function: $y=2^x$
Translated function: $y=2^{x+7}-5$