Question

Which equation is translated 5 units up from f(x) = 3^x

Answer 1

Transformations of Exponential Functions

The parent exponential function is the following:

$f(x)=b^x$, where b is the base.

We can apply many different types of transformations to this function:

$g(x)=a*b^{k(x-d)}+c$

• a ⇒ describes vertical stretch
• k ⇒ describes horizontal stretch
• d ⇒ describes horizontal translation
• c ⇒ describes vertical translation

Solving the Question

In this question, we are working with vertical translation.

• When a function is translated up, c is positive.
• When a function is translated down, c is negative.

We are translating the given function $f(x)=3^x$ 5 units up. This means that we will be adding 5 to the function:

$g(x)=3^x+5$

Answer

a. $g(x)=3^x+5$