Five-Minute Check (over Chapter 6)

CCSS

Then/Now

New Vocabulary

Key Concept: Parent Function of Exponential Growth Functions

Example 1: Graph Exponential Growth Functions

Key Concept: Transformations of Exponential Functions

Example 2: Graph Transformations

Example 3: Real-World Example: Graph Exponential Growth Functions

Key Concept: Parent Function of Exponential Decay Functions

Example 4: Graph Exponential Decay Functions

Example 5: Real-World Example: Graph Exponential Decay Functions

Over Chapter 6

Solve 4a2 – 9 = 0.

A. ± 1

B. ±

C. ± 2

D. 2,

__3

2

__2

3

Over Chapter 6

Solve 6y3 + 13y2 + 5y = 0.

A. 3, 2, 1

B.

C.

D.

Over Chapter 6

A. (f + g)(x) = 3x2 – 70

B. (f + g)(x) = x2 + 3x – 3

C. (f + g)(x) = x2 – 3x + 17

D. (f + g)(x) = 3x – 3

Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10.

Over Chapter 6

A. yes

B. no

Determine whether f(x) = 4x – 9 and g(x) = are inverse functions.

Over Chapter 6

A. –9xy2

B. –9x2y4

C. –3xy2

D. 3xy2

Over Chapter 6

A. –7

B.

C. –2

D. 4

Content Standards

F.IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.8.b Use the properties of exponents to interpret expressions for exponential functions.

Mathematical Practices

3 Construct viable arguments and critique the reasoning of others.

You graphed polynomial functions.

• Graph exponential growth functions.

• Graph exponential decay functions.

• exponential function

• exponential growth

• asymptote

• growth factor

• exponential decay

• decay factor

Graph Exponential Growth Functions

Graph y = 4x. State the domain and range.

Make a table of values. Connect the points to sketch a smooth curve.

Graph Exponential Growth Functions

Answer:

The domain is all real numbers, and the range is all positive real numbers.

Which is the graph of y = 3x?

A. B.

C. D.

Graph Transformations

A. Graph the function y = 3x – 2. State the domain and range.

The equation represents a translation of the graphy = 3x down 2 units.

Graph Transformations

Answer:

Domain = {all real numbers}

Range = {y│y > –2}

Graph Transformations

B. Graph the function y = 2x – 1. State the domain and range.

The equation represents a translation of the graphy = 2x right 1 unit.

Graph Transformations

Answer:

Domain = {all real numbers}

Range = {y │y ≥ 0}

A. Graph the function y = 2x – 4.

A. B.

C. D.

B. Graph the function y = 4x – 2 + 3.

A. B.

C. D.

Graph Exponential Growth Functions

INTERNET In 2006, there were 1,020,000,000 people worldwide using the Internet. At that time, the number of users was growing by 19.5% annually. Draw a graph showing how the number of users would grow from 2006 to 2016 if that rate continued.

First, write an equation using a = 1.020 (in billions), and r = 0.195.

y = 1.020(1.195)t

Then graph the equation.

Graph Exponential Growth Functions

Answer:

CELLULAR PHONES In 2006, there were about 2,000,000,000 people worldwide using cellular phones. At that time, the number of users was growing by 11% annually. Which graph shows how the number of users would grow from 2006 to 2014 if that rate continued?

A. B.

C. D.

Graph Exponential Decay Functions

A. Graph the function State the domain and range.

Graph Exponential Decay Functions

Answer:

Domain = {all real numbers}

Range = {y│y > 0}

Graph Exponential Decay Functions

The equation represents a transformation of the graph

of

B. Graph the function State the domain and range.

Examine each parameter.

● There is a negative sign in front of the function:The graph is reflected in the x-axis.

● a = 4: The graph is stretched vertically.

Graph Exponential Decay Functions

Answer:

Domain = {all real numbers}

Range = {y│y < 2}

● h = 1: The graph is translated 1 unit right.

● k = 2: The graph is translated 2 units up.

A. Graph the function

A. B.

C. D.

B. Graph the function

A. B.

C. D.

Graph Exponential Decay Functions

A. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Draw a graph to represent atmospheric pressure for altitude from 0 to 20 miles.

y = a(1 – r)t

= 14.7(1 – 0.20)t

= 14.7(0.80)t

Graph Exponential Decay Functions

Graph the equation.

Answer:

Graph Exponential Decay Functions

B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Estimate the atmospheric pressure at an altitude of 10 miles.

y = 14.7(0.80)t Equation from part a.

= 14.7(0.80)10 Replace t with 10.

≈ 1.58 lb/in2 Use a calculator.

Answer: The atmospheric pressure at an altitude ofabout 10 miles will be approximately 1.6 lb/in2.

A. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Draw a graph to represent the air pressure for a trip from 0 to 40 miles.

A. B.

C. D.

A. 15.71 lb/in2

B. 16.37 lb/in2

C. 17.43 lb/in2

D. 18.87 lb/in2

B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Estimate the air pressure of the tire after 20 miles.