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Functions and equations - PowerPoint PPT Presentation

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.

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Presentation Transcript

Functions and equations

Mr. ThauvetteDP SL Mathematics

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.

An asymptote is a line that the graph approaches or begins to look

like as it tends to infinity in a particular direction.

x = 2

horizontal asymptote

vertical asymptote

y= 2

To find vertical asymptotes, look for values of x for which the

function is undefined:

• If find where

• If find where

To find horizontal asymptotes, consider the behaviour as

• translates vertically units.

• translates horizontally units.

• translates by the vector

Find the equation of the relation under the translation vector

indicated. Graph both the original and translated relations on the

same set of axes.

(a) (b)

Find the equation of the relation under the translation vector

indicated. Graph both the original and translated relations on the

same set of axes.

(a) (b)

EXAMPLE:

Find the equation of under the translation

Dilation from the x-axis

• is a vertical stretch of

• with dilation factor .

Dilation from the y-axis

• is a horizontal stretch of

• with dilation factor .