Section 7.5 Exponential Functions

Algebra 1

Day 1: Learning Targets• Graph Exponential Function.• Identify data that display exponential

behavior.

Concept

Algebra Lab!

Example 1A. Graph y = 4x. Find the y-intercept and state the domain and range.

Example 1B. Use the graph of y = 4x to determine the approximate value of 41.5.

The graph represents all real values ofx and their corresponding values of y for y = 4x.

Answer: The value of y is 8 when x = 1.5.

Use a calculator to confirm this value.

41.5 = 8

Example 2A. Graph y = 5x. Find the y-intercept and state the domain and range.

Example 2B. Use the graph of y = 5x to determine the approximate value of 51.5.

Answer: The value of y is about 11 when x = 1.5.

Use a calculator to confirm this value.

51.5 = 11.1803398875

Example 3A. Graph y = (1/4)x. Find the y-intercept and state the domain and range.

Example 3

Use a calculator to confirm this value.

Answer: The value of y is about 8 when x = –1.5.

Example 4A. Graph y = (1/5)x. Find the y-intercept and state the domain and range.

Example 5A. Find the graph of A. B.

C. D.

Example 5

A. about 1

B. about 3

C. about 2

D. about 0.1

Example 6A.) Determine whether the set of data displays exponential behavior. Explain why or why not.

Method 1 Look for a pattern.

The domain values are at regular intervals of 10. Look for a common factor among the range values.

10 25 62.5 156.25

× 2.5 × 2.5 × 2.5 Answer: Since the domain values are at regular

intervals and the range values differ by a positive common factor, the data are probably exponential. The equation for the data may involve (2.5)x.

Example 6Method 2 Graph the data.Answer: The graph

shows rapidly increasing values of y as x increases. This is a characteristic of exponential behavior.

Example 6B

A. no

B. yes

C. cannot be determined

Determine whether the set of data displays exponential behavior.

Homework7.5 Day 1 Worksheet.

Day 2: Learning Targets• Graph Exponential Function with translations.

• Write equations for graphs.

Algebra Lab!

Example 1Graph y = 3(2)x. Find the y-intercept and state the domain and range.

Example 2Graph y = 3(2)x. Find the y-intercept and state the domain and range.

Write an equation for the graph.

MAKE A TABLE.x

y

EQUATION:

Write an equation for the graph.

MAKE A TABLE.x

y

EQUATION:

Write an equation for the graph.

MAKE A TABLE.x

y

EQUATION:

Homework7.5 Day 2 Worksheet.