# Lesson 13

Representations of Exponential Functions

- Let’s get information about a function from its graph.

### 13.1: Which One Doesn’t Belong?: Representations of Functions

Which one doesn’t belong?

C: \(f(t)=20 \boldcdot 2^t\)

### 13.2: Interrogating Function Representations

- Consider the graph of \(f(x)=3 \boldcdot 2^x\) and corresponding table.
\(x\) \(f(x)\) 0 3 1 6 2 12 - Using the first two points, what is the growth factor?
- Using the second two points, what is the growth factor?
- Where do you see this growth factor in the equation?
- Where do you see the growth factor on the graph?
- What is the vertical intercept of the graph?
- How can you tell from the equation that this is the vertical intercept?

- Consider the graph of \(g(x)=8 \boldcdot \left( \frac12 \right)^x\) and corresponding table.
\(x\) \(g(x)\) 0 8 1 4 2 2 - Using the first two points, what is the growth factor?
- Using the second two points, what is the growth factor?
- Where do you see this growth factor in the equation?
- Where do you see the growth factor on the graph?
- What is the vertical intercept of the graph?
- How can you tell from the equation that this is the vertical intercept?

### 13.3: Matching Representations of Exponential Functions

- Match each function with the graph that represents it.
\(a(t)=300 \boldcdot 2^t\)

\(b(t)=300 \boldcdot 3^t\)

\(c(t)=300 \boldcdot \left( \frac12 \right)^t\)

\(d(t)=300 \boldcdot \left( \frac13 \right)^t\)

\(e(t)=108 \boldcdot 2^t\)

\(f(t)=108 \boldcdot 3^t\)

\(g(t)=108 \boldcdot \left( \frac12 \right)^t\)

\(h(t)=108 \boldcdot \left( \frac13 \right)^t\)

- On two of the graphs, show where you can see the vertical intercept: 108 and 300.
- On four of the graphs, show where you can see the growth factor: \(\frac13\), \(\frac12\), 2, and 3.