Functions and equations

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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

Graphs of Functions

To find vertical asymptotes, look for values of x for which thefunction is undefined:

• 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.

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 (b)

• 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 (b)

Summary

• translates by the vector

EXAMPLE:

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 y-axis

• is a horizontal stretch of with dilation factor .

Dilation from the y-axis

Reflections

Reflection about the x-axis

Reflection about the y-axis

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