Functions and equations
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FUNCTIONS AND EQUATIONS Mr. Thauvette DP SL Mathematics
description
Functions and equations. Mr. Thauvette DP SL Mathematics. Graphs of Functions. The x -intercepts of a function are the values of x for which y = 0. They are the zeros (i.e., solutions, roots) of the function. The y -intercept of a function is the value of y when x = 0. - PowerPoint PPT Presentation
Transcript of Functions and equations
FUNCTIONS AND EQUATIONS
Mr. ThauvetteDP SL Mathematics
Graphs of Functions
The x-intercepts of a function are the values of x for which y = 0. They are the zeros (i.e., solutions, roots) of the function.
The y-intercept of a function is the value of y when x = 0.
Graphs of Functions
An asymptote is a line that the graph approaches or begins to looklike as it tends to infinity in a particular direction.
vertical asymptote horizontal asymptotey = 2
x = 2
Graphs of Functions
To find vertical asymptotes, look for values of x for which thefunction is undefined:
• If find where
• If find where
To find horizontal asymptotes, consider the behaviour as
Transformations of Graphs• translates vertically units.
• translates horizontally units.
• translates by the vector
• translates vertically units.
• translates vertically units.
• translates vertically units.
• translates vertically units.
Examples
Find the equation of the relation under the translation vectorindicated. Graph both the original and translated relations on the same set of axes.
(a) (b)
Example (a)
Example (a)
Example (b)
Example (b)
• translates horizontally units.
• translates horizontally units.
• translates horizontally units.
• translates horizontally units.
Examples
Find the equation of the relation under the translation vectorindicated. Graph both the original and translated relations on the same set of axes.
(a) (b)
Example (a)
Example (a)
Example (b)
Example (b)
Summary
• translates by the vector
EXAMPLE:
Find the equation of under the translation
Find the equation of under the translation
Dilation from the x-axis
• is a vertical stretch of with dilation factor .
Dilation from the x-axis
Dilation from the x-axis
Dilation from the x-axis
Dilation from the x-axis
Dilation from the x-axis
Dilation from the y-axis
• is a horizontal stretch of with dilation factor .
Dilation from the y-axis
Dilation from the y-axis
Dilation from the y-axis
Dilation from the y-axis
Dilation from the y-axis
Reflections
Reflection about the x-axis
Reflection about the y-axis
