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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 look

like as it tends to infinity in a particular direction.

x = 2

horizontal asymptote

vertical asymptote

y= 2

Graphs of Functions

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

Transformations of Graphs

- translates vertically units.

- translates horizontally units.

- translates by the vector

Examples

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)

Examples

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)

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 .

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