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MAT 150 Algebra Class #12 Topics: • Transformations of Graphs of Functions • Symmetric about the y- axis, x-axis or origin • Is a function odd, even or neither?

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Page 1: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

MAT 150 AlgebraClass #12

Topics:• Transformations of

Graphs of Functions• Symmetric about the y-

axis, x-axis or origin• Is a function odd, even

or neither?

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=dhiT_VNOBU-y5M&tbnid=3Fo2CWDh9Ud-9M:&ved=0CAUQjRw&url=http://facweb.cti.depaul.edu/cwhite/LSP%20120/Lectures,%20Activities,%20Homework.htm&ei=OPnIUZf5H4SD0QHu0YHoAw&bvm=bv.48293060,d.dmg&psig=AFQjCNHIo1pcnLfdwF1MMobrzvy0wSzimg&ust=1372211822953344

Page 2: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

Parent Functions Function Identify Sketch

Linear

Quadratic

Square Root

Rational

Power

Logarithm

Absolute Value

Cubic

Page 3: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

Transformation of Graphs of Functions

Type of Shift Mathematical Language

VerbalLanguage

Vertical Shifts y = f(x) + k Graph is shifted k units up if k > 0 and k

units down if k< 0

Horizontal Shifts y = f(x – h) Graph is shifted h units right if h > 0 and

h units left if h < 0.

Stretching y = a* f(x) Graph is vertically stretched using a

factor of |a| if |a|> 1.

Page 4: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

Transformation of Graphs of Functions

Type of Shift Mathematical Language

VerbalLanguage

Compressing y = a* f(x) Graph is vertically stretched using a

factor of |a| if |a|< 1.

Reflections x-axis y = -f(x) Graph is reflected across the x-axis.

Reflection y-axis Y = f(-x) Graph is reflected across the y-axis.

Page 5: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

ExampleUse the function to answer the following questions.

a. The graph of this function is a shift graph of which basic function?

b. Describe the transformations used to obtain the graph of the function.

c. Sketch a graph of the function.

Page 6: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

Symmetry Symmetry Mathematic

al Language VerbalLanguage

Respect to y-axis f(-x) = f(x) If every point (x, y) on the graph, the point (-x , y) is also on the graph. Such a function is called an EVEN FUNCTION.

Respect to the origin f(-x) = -f(x) If every point (x, y) on the graph, the point (-x , -y) is also on the graph. Such a function is called an ODD FUNCTION.

Respect to x-axis If every point (x, y) on the graph, the point (x , - y) is also on the graph.

Page 7: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

ExamplesDetermine algebraically whether the graph of the given equation is symmetric with respect to x-axis, y-axis and/or the origin. Is the function even, odd or neither? Confirm graphically.

Page 8: MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

AssignmentPg. 259#3-9odd#17-18#23 & 25#27-35 odd#51, 60

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