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Holt Geometry 3-1 Lines and Angles A-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on.

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Presentation on theme: "Holt Geometry 3-1 Lines and Angles A-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on."— Presentation transcript:

1 Holt Geometry 3-1 Lines and Angles A-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F-FB.B.3Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

2 Holt Geometry 3-1 Lines and Angles  Branch  Reciprocal function

3 Holt Geometry 3-1 Lines and Angles  Paper for notes  Graph paper  Pearson 8.2  Graphing Calc.

4 Holt Geometry 3-1 Lines and Angles TOPIC: 8.2 The Reciprocal Function Family Name: Daisy Basset Date : Period: Subject: Notes Objective: Identify the effect on the graph of replacing f(x) by f(x) + k and f(x+h) for specific values of h and k (both positive and negative).

5 Holt Geometry 3-1 Lines and Angles Key Concepts  General Form of the Reciprocal Function Family  The Reciprocal Function Family

6 Holt Geometry 3-1 Lines and Angles 1.What is the graph of, ? Identify the x- and y- intercepts and the asymptotes of the graph. State the domain and range of the function.

7 Holt Geometry 3-1 Lines and Angles Make a table of values that includes + and – values. Choose values of x that divide easily into 12. xy -10 -8 -6 -4 -3 -2 xy 2 3 4 6 8 10

8 Holt Geometry 3-1 Lines and Angles x y -8-1.5 -6-2 -4-3 -4 -2-6 26 34 43 62 81.5 Graph the points.

9 Holt Geometry 3-1 Lines and Angles Since the denominator ≠ 0, Since the numerator is never 0, The horizontal asymptote is the there is no y-intercept. there is no x-intercept. x-axis. The vertical asymptote is they-axis.

10 Holt Geometry 3-1 Lines and Angles The domain is The range is all real #’s, x ≠ 0. all real #’s, y ≠ 0.

11 Holt Geometry 3-1 Lines and Angles 2.For each given value of a, how do the graphs of and compare? What is the effect of a on the graph?

12 Holt Geometry 3-1 Lines and Angles Sketch the graphs. A. The graph of is a stretch of the graph of by the factor 6.

13 Holt Geometry 3-1 Lines and Angles Sketch the graphs. B. The graph of is a shrink of the graph of by the factor 0.25.

14 Holt Geometry 3-1 Lines and Angles Sketch the graphs. C. The graph of is a stretch by the factor 6 followed by a reflection across the x-axis.

15 Holt Geometry 3-1 Lines and Angles  Notes 8.2  Graph paper  Graphing Calc.

16 Holt Geometry 3-1 Lines and Angles 3.What is the graph of ? Identify the domain and range.

17 Holt Geometry 3-1 Lines and Angles Find h and k using the standard form. For, h = and k =. -4 -6 Sketch the asymptotes. Vertical asymptote Horizontal asymptote

18 Holt Geometry 3-1 Lines and Angles h = -4 k = -6

19 Holt Geometry 3-1 Lines and Angles The graph of contains the points (1, 1) and (-1, -1).

20 Holt Geometry 3-1 Lines and Angles (1, 1 ) (-1, -1 ) Translate the points and curves, _________ and __ _________. The points are (-3, -5) and (-5, -7). 4 units left units down 6 - 6 - 4

21 Holt Geometry 3-1 Lines and Angles The points are (-3, -5) and (-5, -7).

22 Holt Geometry 3-1 Lines and Angles The domain is The range is all real #’s, x ≠ -4. all real #’s, y ≠ -6.

23 Holt Geometry 3-1 Lines and Angles 4.This graph of a function is a translation of the graph of. What is an equation for the function?

24 Holt Geometry 3-1 Lines and Angles The asymptotes are x = and y =. -3 4 So, h = -3, k = 4.

25 Holt Geometry 3-1 Lines and Angles a = h = k =2 -3 4

26 Holt Geometry 3-1 Lines and Angles SummarySummarize/reflect D What did I do? L What did I learn? I What did I find most interesting? Q What questions do I still have? What do I need clarified?

27 Holt Geometry 3-1 Lines and Angles TOPIC: 8.3 Rational Functions & Their Graphs Name: Daisy Basset Date : Period: Subject: Notes Objective: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

28 Holt Geometry 3-1 Lines and Angles Vocabulary  Rational Function  Continuous Graph  Discontinuous Graph

29 Holt Geometry 3-1 Lines and Angles Key Concepts  Point of Discontinuity  Vertical Asymptotes of Rational Functions  Horizontal Asymptotes of Rational Functions

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