Algebra 2 7-3 Complete Lesson: Logarithmic Functions as Inverses

Last updated over 4 years ago

38 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

A.SSE.1.b

F.BF.4.a

F.IF.8.b

F.IF.1

F.IF.5

A.SSE.1.b

F.IF.1

A.SSE.1.b

F.BF.4.a

F.IF.7.e

A.SSE.3.a

A.SSE.3.c

A.SSE.1.b

100

A.SSE.1.b

F.BF.4.a

Algebra 2 7-3 Complete Lesson: Logarithmic Functions as Inverses

Last updated over 4 years ago

38 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Solve It! The chart shows different ways you can write 4 and 16 in the form a^b, in which a and b are integers and a ≠ 1.
What is the smallest number you can write in this a^b form in four different ways? In five different ways? In seven different ways?

64
4096
16,777,216
24,287,916

In four different ways
In five different ways
In seven different ways

A.SSE.1.b

F.BF.4.a

F.IF.8.b

Problem 1 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.9

Problem 1 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.9

Problem 1 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.9

Problem 2 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.8.b

Problem 2 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.8.b

Problem 2 Got It?

A.SSE.1.b

F.BF.4.a

F.IF.8.b

Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

F.IF.8.b

F.LE.5

Problem 4 Got It? What is the graph of y = log₄x ? Identify the domain, range, y-intercept, and asymptote(s).

Domain: x > 0
Domain: x > 4
Range: y > 0
Range: all real numbers
y-intercept: 4
No y-intercept
Vertical asymptote: x = 0
No asymptotes

Graph of y = log₄x
Domain of y = log₄x
Range of y = log₄x
y-intercept of y = log₄x
Asymptote(s) of y = log₄x

F.IF.1

F.IF.5

Problem 4 Got It? Reasoning: Suppose you use the table to help you graph y = log₂x. (Recall that if y = log₂x, then 2^y = x.) Complete the table.

F.BF.4.a

A.SSE.1.b

F.BF.4.a

F.IF.9

Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

Translate 3 units right
Translate 3 units left
Translate 4 units down
Translate 4 units up
Domain, range, and asymptote remain the same
Domain changes from x > 0 to x > 3
Range remains all real numbers
Asymptote changes from x = 0 to x = 3
Stretch vertically by a factor of 3

A.SSE.1.b

F.IF.1

A.SSE.1.b

F.BF.4.a

F.IF.9

A.SSE.1.b

F.BF.4.a

F.IF.9

A.SSE.1.b

F.BF.4.a

F.IF.9

A.SSE.1.b

F.BF.4.a

F.IF.9

A.SSE.1.b

F.BF.4.a

F.IF.8.b

A.SSE.1.b

F.BF.4.a

F.IF.8.b

A.SSE.1.b

F.BF.4.a

F.IF.8.b

A.SSE.1.b

F.BF.4.a

F.IF.8.b

Vocabulary: Determine whether the logarithm is a common logarithm.

Common logarithm

Not a common logarithm

A.SSE.1.b

Vocabulary: Determine whether the logarithm is a common logarithm.

Not a common logarithm

Common logarithm

A.SSE.1.b

Vocabulary: Determine whether the logarithm is a common logarithm.

Not a common logarithm

Common logarithm

A.SSE.1.b

Vocabulary: Determine whether the logarithm is a common logarithm.

Not a common logarithm

Common logarithm

A.SSE.1.b

F.BF.4.a

Compare and Contrast: Compare the graph of the functions.
How are the graphs alike? How are they different?
Complete your response to this item using what you know about translating logarithmic functions before graphing both functions on the embedded Desmos graphing calculator below.
Revise your response, if necessary.

F.IF.7.e

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

F.IF.7.e

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

F.IF.7.e

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

F.IF.7.e

Review Lesson 4-4: Factor the expression.

A.SSE.3.a

Review Lesson 4-4: Factor the expression.

A.SSE.3.a

Review Lesson 1-3: Evaluate each expression for the given value of the variable.

A.SSE.3.c

Vocabulary Review: Identify the base in each power.

x
x - 2
-2
2
4x
4

The base of the power
The base of the power
The base of the power

A.SSE.1.b

Use Your Vocabulary: Match each logarithmic expression with its description in words.

log base x of y
log base 3 of 4
log base 4 of 3
log base y of x

100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

A.SSE.1.b

F.BF.4.a

Algebra 2 7-3 Complete Lesson: Logarithmic Functions as Inverses

Algebra 2 7-3 Complete Lesson: Logarithmic Functions as Inverses

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1. What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

Problem 4 Got It? What is the graph of y = log4x ? Identify the domain, range, y-intercept, and asymptote(s).

Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 4-4: Factor the expression.

Review Lesson 4-4: Factor the expression.

Review Lesson 1-3: Evaluate each expression for the given value of the variable.

Vocabulary Review: Identify the base in each power.

Use Your Vocabulary: Match each logarithmic expression with its description in words.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1. What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

Problem 4 Got It? What is the graph of y = log4x ? Identify the domain, range, y-intercept, and asymptote(s).

Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Vocabulary: Determine whether the logarithm is a common logarithm.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 7-2: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 4-4: Factor the expression.

Review Lesson 4-4: Factor the expression.

Review Lesson 1-3: Evaluate each expression for the given value of the variable.

Vocabulary Review: Identify the base in each power.

Use Your Vocabulary: Match each logarithmic expression with its description in words.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! The chart shows different ways you can write 4 and 16 in the form a^b, in which a and b are integers and a ≠ 1.
What is the smallest number you can write in this a^b form in four different ways? In five different ways? In seven different ways?

Problem 4 Got It? What is the graph of y = log₄x ? Identify the domain, range, y-intercept, and asymptote(s).

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Solve It! The chart shows different ways you can write 4 and 16 in the form a^b, in which a and b are integers and a ≠ 1.
What is the smallest number you can write in this a^b form in four different ways? In five different ways? In seven different ways?

Problem 4 Got It? What is the graph of y = log₄x ? Identify the domain, range, y-intercept, and asymptote(s).

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.