1 / 27

Pre-Algebra HOMEWORK

Pre-Algebra HOMEWORK. Page 636-637 #1-7 & #15-20. Students will be able to solve sequences and represent functions by completing the following assignments. Learn to find terms in an arithmetic sequence . Learn to find terms in a geometric sequence . Learn to find patterns in sequences .

scasillas
Télécharger la présentation

Pre-Algebra HOMEWORK

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pre-Algebra HOMEWORK Page 636-637 #1-7 & #15-20

  2. Students will be able to solve sequences and represent functions by completing the following assignments. • Learn to find terms in an arithmetic sequence. • Learn to find terms in a geometric sequence. • Learn to find patterns in sequences. • Learn to represent functions with tables, graphs, or equations.

  3. Today’s Learning Goal Assignment Learn to represent functions with tables, graphs, or equations.

  4. Functions 12-4 Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  5. Functions 12-4 8 3 5 4 1, , , , 3 3 2 5 2n n + 1 Pre-Algebra Warm Up 1. Give the next three terms in each sequence using the simplest rule you can find. 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, . . . Find the first five terms of the sequence defined by the given rule. 2.an = 3.an = n(n – 1) 1, 13, 1, 15 0, 2, 6, 12, 20

  6. Problem of the Day What is the 1,111,111th term of the geometric sequence defined by a1 = 1, r = –1? 1; every odd term is 1, and every even term is –1.

  7. Vocabulary function input output domain range function notation

  8. A function is a rule that relates two quantities so that each input value corresponds to exactly one output value. The domain is the set of all possible input values, and the range is the set of all possible output values.

  9. Functions can be represented in many ways, including tables, graphs, and equations. If the domain of a function has infinitely many values, it is impossible to represent them all in a table, but a table can be used to show some of the values and to help in creating a graph.

  10. Additional Example 1: Finding Different Representations of a Function Make a table and a graph of y = 3 – x2. Make a table of inputs and outputs. Use the table to make a graph. 3 – (–2)2 –1 3 – (–1)2 2 3 – (0)2 3 3 – (1)2 2 –1 3 – (2)2

  11. y 3 x 2 –3 Try This: Example 1 Make a table and a graph of y = x + 1. Make a table of inputs and outputs. Use the table to make a graph. –1 + 1 0 0 + 1 1 1 + 1 2 2 + 1 3

  12. To determine if a relationship is a function, verify that each input has exactly one output.

  13. Additional Example 2A: Identifying Functions Determine if the relationship represents a function. A. The input x = 2 has two outputs, y = 3 and y = 6. The input x = 3 also has more than one output. The relationship is not a function.

  14. Try This: Example 2A Determine if the relationship represents a function. A. Each input x has only one output y. The relationship is a function.

  15. Additional Example 2B: Identifying Functions Determine if the relationship represents a function. B. The input x = 0 has two outputs, y = 2 and y = –2. Other x-values also have more than one y-value. The relationship is not a function.

  16. y x Try This: Example 2B Determine if the relationship represents a function. B. Since the relationship is linear there can only be one output y for each input x. The relationship is a function.

  17. Additional Example 2C: Identifying Functions Determine if the relationship represents a function. C. y = x3 Make an input-output table and use it to graph y = x3. Each input x has only one output y. The relationship is a function.

  18. Try This: Example 2C Determine if the relationship represents a function. C. y = x – 1 Each input x has only one output y. The relationship is a function.

  19. Reading Math f(x) is read “f of x.” f(1) is read “f of 1.” You can describe a function using function notation. In function notation, the output value of the function f that corresponds to the input value x is written as f(x). The expression f(x) means “the rule of f applied to the value of x,” not “f multiplied by x.”

  20. Additional Example 3A: Evaluating Functions For the function, find f(0), f(-2), and f(1). A. y = 3x + 2 f(x) = 3x + 2 Write in function notation. f(0) = 3(0) + 2 = 2 f(–2) = 3(–2) + 2 = –4 f(1) = 3(1) + 2 = 5

  21. Try This: Example 3A For the function, find f(0), f(-1), and f(1). A. y = 2x + 2 f(x) = 2x + 2 Write in function notation. f(0) = 2(0) + 2 = 2 f(–1) = 2(–1) + 2 = 0 f(1) = 2(1) + 2 = 4

  22. Additional Example 3B: Evaluating Functions For the function, find f(0), f(-2), and f(1). B. Read the graph to find y for each x. f(x) = y f(0) = –1 f(–2) = 1 f(1) = –2

  23. Try This: Example 3B For each relationship, find f(–3), f(-1), and f(2). B. Read the graph to find y for each x. f(x) = y f(–3) = 2 f(–2) = 1 f(2) = –3

  24. Additional Example 3C: Evaluating Functions For the function, find f(0), f(-2), and f(1). C. Read the table to find y for each x. f(x) = y f(0) = 4 f(–2) = 6 f(1) = 3

  25. Try This: Example 3C For the function, find f(0), f(-1), and f(1). C. Read the table to find y for each x. f(x) = y f(0) = 0 f(–1) = 4 f(1) = 2

  26. y 4 2 x -4 -2 2 4 -2 -4 Lesson Quiz: Part 1 1. Graph the function y = x2 – 3.

  27. Lesson Quiz: Part 2 Determine if each relationship represents a function. 2. 3.y = 3x + 5 4. For the function y = 3x2 – 2, find f(0), f(2), and f(–4). no yes –2, 10, 46

More Related