### Home > PC3 > Chapter 5 > Lesson 5.2.3 > Problem5-89

5-89.

Consider the function $h(x)=3(2)^x+1$.

1. Describe $h(x)$ as a transformation of $y=2^x$.

The function is vertically _____ by a factor of __ and shifted __ $1$ unit.

2. Sketch the graph of $y=h(x)$.

This is an exponential growth function. The locator point is at $(0,?)$.

3. What is the equation of the horizontal asymptote?

Use your graph from part (b). You can use a graphing calculator to verify that your graph is correct. If it is not, be sure to identify and correct any mistakes.

4. What is the $y$-intercept?

Solve: $y=3(2)^0+1$

5. What is the $y$-intercept of the graph of $y=a(2)^x+k$?

Solve: $y=a(2)^0+k$