CCSS TP Algebra I Unit 5

Walch Education, 20.10.2015

These applets are provided by Walch Education as supplemental material for the [i]CCSS Traditional Pathway: Algebra I[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

Inhaltsverzeichnis

  1. Lesson 1
    1. Example 1
    2. Example 2
  2. Lesson 2
    1. Example 1
    2. Example 2
    3. Example 1
    4. Example 2
    5. Example 1
    6. Example 2
  3. Lesson 3
    1. Example 2
    2. Example 4
    3. Example 1
    4. Example 3
  4. Lesson 4
    1. Example 1
    2. Example 2
    3. Example 1
    4. Example 3
  5. Lesson 5
    1. Example 1
    2. Example 3
    3. Example 1
    4. Example 2
  6. Lesson 6
    1. Example 1
    2. Example 2
    3. Example 1
    4. Example 2
    5. Example 1
    6. Example 2
  7. Lesson 7
    1. Example 1
    2. Example 3
    3. Example 2
    4. Example 3
  8. Lesson 8
    1. Example 1
    2. Example 3

1.

Lesson 1

  • 1. Example 1
  • 2. Example 2

1.1.

Example 1

Simplify the expression [math]a^{\frac{6}{5}} \bullet a^{\frac{3}{2}}[/math].

[list=1] [*]Identify which property can be used to simplify the expression. [*]Apply the property to simplify the expression. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

1.2.

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2.

Lesson 2

  • 1. Example 1
  • 2. Example 2
  • 3. Example 1
  • 4. Example 2
  • 5. Example 1
  • 6. Example 2

2.1.

Example 1

A local store’s monthly revenue from T-shirt sales is modeled by the function [math]f(x) = –5x^2 + 150x – 7[/math].Use the equation and graph to answer the following questions: At what prices is the revenue increasing? Decreasing? What is the maximum revenue? What prices yield no revenue? Is the function even, odd, or neither?

[list=1] [*]Determine when the function is increasing and decreasing. [*]Determine the maximum revenue. [*]Determine the prices that yield no revenue. [*]Determine if the function is even, odd, or neither. [*]Use the graph of the function to verify that the function is neither odd nor even. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

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2.4.

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2.5.

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2.6.

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3.

Lesson 3

  • 1. Example 2
  • 2. Example 4
  • 3. Example 1
  • 4. Example 3

3.1.

Example 2

Given the function [math]f(x) = –2x^2 + 16x – 30[/math], identify the key features of the graph: the extremum, vertex, and [math]y[/math]-intercept. Then sketch the graph.

[list=1] [*]Determine the extremum of the graph. [*]Determine the vertex of the graph. [*]Determine the [math]y[/math]-intercept of the graph. [*]Graph the function. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

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3.3.

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3.4.

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4.

Lesson 4

  • 1. Example 1
  • 2. Example 2
  • 3. Example 1
  • 4. Example 3

4.1.

Example 1

A farmer is building a rectangular pen using [math]100[/math] feet of electric fencing and the side of a barn. In addition to fencing, there will be a [math]4[/math]-foot gate also requiring the electric fencing on either side of the pen. The farmer wants to maximize the area of the pen. How long should he make each side of the fence in order to create the maximum area?
[list=1][br][*]Write the expressions that describe the length of each side of the pen.[br][/*][*]Build the equation that describes the area of the pen.[br][/*][*]To find the maximum area, use the vertex.[br][/*][*]Finally, use the [math]x[/math]-value from the vertex to find the lengths of each side of the pen.[br][/*][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.
– Walch Education

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4.4.

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5.

Lesson 5

  • 1. Example 1
  • 2. Example 3
  • 3. Example 1
  • 4. Example 2

5.1.

Example 1

Consider the function [math]f(x) = x^2[/math] and the constant [math]k = 2[/math]. What is [math]f(x) + k[/math]? How are the graphs of [math]f(x)[/math] and [math]f(x) + k[/math] different?

[list=1] [*]Substitute the value of [math]k[/math] into the function. [*]Use a table of values to graph the functions on the same coordinate plane. [*]Compare the graphs of the functions. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

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5.3.

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5.4.

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6.

Lesson 6

  • 1. Example 1
  • 2. Example 2
  • 3. Example 1
  • 4. Example 2
  • 5. Example 1
  • 6. Example 2

6.1.

Example 1

The function [math]y = 0.176 \sqrt{x + 30}[/math] has a domain of [math]–30 ≤ x ≤ 0[/math]. Determine the range of the function, then use a graph to estimate the value of [math]y[/math] when [math]x = –10[/math].

[list=1] [*]Determine the range of the function. [*]Find at least three points on the function, including critical points. [*]Plot the three points and sketch the graph. [*]Use the graph to estimate the function’s output at the given input. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

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6.3.

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6.4.

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6.5.

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6.6.

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7.

Lesson 7

  • 1. Example 1
  • 2. Example 3
  • 3. Example 2
  • 4. Example 3

7.1.

Example 1

A school tracks the total number of students enrolled each year. The school uses the change in the total number of students to estimate how many students have been enrolled in the school each year since 2000. If [math]t[/math] is the number of years after 2000, the total number of students, [math]f(t)[/math], can be estimated using the function [math]f(t) = 250(0.98)^t[/math]. How is the total number of students changing each year? Is the total number of students growing or decaying?
[list=1][br][*]Identify the yearly rate of change in the function.[br][/*][*]Describe how the rate of change relates to the change of the dependent quantity.[br][/*][*]Determine whether the dependent quantity is growing or decaying.[br][/*][/list][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.
– Walch Education

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7.4.

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8.

Lesson 8

  • 1. Example 1
  • 2. Example 3

8.1.

Example 1

Lana is driving home from her friend’s house. She is driving at a steady speed, and her distance from her home, in miles, can be represented by the function [math]f(x) = –40x + 15[/math], where [math]x[/math] is her driving time in hours. Find the inverse function [math]f^{–1}(x)[/math] to show when, in hours, Lana will be [math]x[/math] miles from home.
[list=1][br][*]Determine if the function is one-to-one.[br][/*][*]Rewrite the function [math]f(x)[/math] in the form “[math]y =[/math].”[br][/*][*]Switch [math]x[/math] and [math]y[/math] in the original equation of the function.[br][/*][*]Solve the new equation for [math]y[/math] by using inverse operations.[br][/*][*]Replace [math]y[/math] with [math]f^{–1}(x)[/math] to show that the equation is the inverse of [math]f(x)[/math].[br][/*][/list][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.
– Walch Education

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