U2D8 Graphing Exponential and Log Functions Feb3

Instructions

In this lesson we will learn several ways to graph exponential and logarithmic functions.

1

MODELING REAL LIFE
Skydivers use an altimeter to track their altitudes as they fall. The altimeter determines altitude by measuring air pressure. The altitude h (in meters) above sea level is related to the air pressure P (in pascals) by the function shown in the diagram. What is the altitude above sea level when the air pressure is 57,000 pascals? (Round your answer to the nearest hundredths.)

MODELING REAL LIFE 
The energy magnitude of an earthquake can be modeled by 
where x is the amount of energy released (in ergs).

1

In 2019, an earthquake near Ridgecrest, California released 3.16 x 1025 ergs. What was the energy magnitude of the earthquake?

The energy magnitude of the earthquake was _______.  (Round your answer to the nearest tenth.)

1

Find and interpret f −1(x).

1

Use technology to graph f and f−1. Find the asymptotes and when the function is positive, negative, increasing, or decreasing.

Evaluate each problem.

1

_______ 

1

_______ 

1

_______ 

1

_______ 

1

_______ 

1

_______ 

1

Use asymptotes and transformations to match each function to its graph.

Draggable item		Corresponding Item

1

You Try!
Try finding the asymptote and graphing two coordinates.

1

You Try!
Try finding the asymptote and graphing two coordinates.

ERROR ANALYSIS 
Describe and correct the error in graphing the transformation of f represented by g.

1

1

Match each function to its graph. Use transformations to help you figure it out.

Draggable item		Corresponding Item

The graph of g is a transformation of the graph of f(x) = 3x.

This is the graph of g. You can look up the graph for f(x) = 3x.

1

How was g transformed from f?

1

The function g(x) can be written as 
g(x) = _______.

1

What do we get when x = 0 in the g function?
Another way to ask:
Find g(0), this means plug 0 in for x to get y.
 g(0) = _______ 

1

What do we get when x = 1 in the g function?
Another way to ask:
Find g(1), this means plug 0 in for x to get y.
g(1) =_______.

Find and interpret f −1(x).

Use technology to graph f and f−1. Find the asymptotes and when the function is positive, negative, increasing, or decreasing.

Use asymptotes and transformations to match each function to its graph.

You Try!Try finding the asymptote and graphing two coordinates.

You Try!Try finding the asymptote and graphing two coordinates.

Match each function to its graph. Use transformations to help you figure it out.

How was g transformed from f?

You Try!
Try finding the asymptote and graphing two coordinates.

You Try!
Try finding the asymptote and graphing two coordinates.