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

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Posljednje ažuriranje over 4 years ago
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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.

10
A.SSE.1.b
F.BF.4.a
F.IF.8.b
10
F.IF.1
F.IF.5
…
21
A.SSE.1.b
F.IF.1
…
5
A.SSE.1.b
5
A.SSE.1.b
5
A.SSE.1.b
5
A.SSE.1.b
10
A.SSE.1.b
F.BF.4.a
…
20
F.IF.7.e
5
F.IF.7.e
5
F.IF.7.e
5
F.IF.7.e
10
A.SSE.3.a
10
A.SSE.3.a
10
A.SSE.3.c
10
A.SSE.1.b
10
100
10
A.SSE.1.b
F.BF.4.a
…
Pitanje 1
1.

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?

  • 64

  • 4096

  • 16,777,216

  • 24,287,916

  • In four different ways

  • In five different ways

  • In seven different ways

10
Pitanje 2
2.

Problem 1 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.9
10
Pitanje 3
3.

Problem 1 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.9
10
Pitanje 4
4.

Problem 1 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.9
10
Pitanje 5
5.

Problem 2 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.8.b
10
Pitanje 6
6.

Problem 2 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.8.b
10
Pitanje 7
7.

Problem 2 Got It?

A.SSE.1.b
F.BF.4.a
F.IF.8.b
10
Pitanje 8
8.

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
Pitanje 9
9.

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

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

2
F.BF.4.a
2
F.BF.4.a
2
F.BF.4.a
2
A.SSE.1.b
F.BF.4.a
F.IF.9
Pitanje 14
14.

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

5
Pitanje 15
15.
A.SSE.1.b
F.BF.4.a
F.IF.9
5
Pitanje 16
16.
A.SSE.1.b
F.BF.4.a
F.IF.9
5
Pitanje 17
17.
A.SSE.1.b
F.BF.4.a
F.IF.9
5
Pitanje 18
18.
A.SSE.1.b
F.BF.4.a
F.IF.9
5
Pitanje 19
19.
A.SSE.1.b
F.BF.4.a
F.IF.8.b
5
Pitanje 20
20.
A.SSE.1.b
F.BF.4.a
F.IF.8.b
5
Pitanje 21
21.
A.SSE.1.b
F.BF.4.a
F.IF.8.b
5
Pitanje 22
22.
A.SSE.1.b
F.BF.4.a
F.IF.8.b
Pitanje 23
23.

Vocabulary: Determine whether the logarithm is a common logarithm.

Pitanje 24
24.

Vocabulary: Determine whether the logarithm is a common logarithm.

Pitanje 25
25.

Vocabulary: Determine whether the logarithm is a common logarithm.

Pitanje 26
26.

Vocabulary: Determine whether the logarithm is a common logarithm.

Pitanje 28
28.

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.

Pitanje 29
29.

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

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.
Pitanje 30
30.

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

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.
Pitanje 31
31.

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

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.
Pitanje 32
32.

Review Lesson 4-4: Factor the expression.

Pitanje 33
33.

Review Lesson 4-4: Factor the expression.

Pitanje 34
34.

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

  • ¼

  • 2

  • 256

Pitanje 35
35.

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

Pitanje 36
36.

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

Pitanje 37
37.

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.

Pitanje 38
38.

Reflection: Math Success

Pitanje 10
10.
Pitanje 11
11.
Pitanje 12
12.
Pitanje 13
13.