How do I find the stretches of a transformed function?

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How do I find the stretches of a transformed function?

Do I look for the x and y intercepts and the invariant points?

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Answer 1 · 2018-02-09T01:44:02

Look at the variables of $a$ $a$ and $b$ $b$ to figure out what factor to stretch by.

Explanation:

Refer to: $y = a f (b (x - h)) + k$ $y=af(b(x-h))+k$

A vertical stretch is the stretching of a function on the x-axis.
If $| a | > 1$ $|a|>1$ , then the graph is stretched vertically by a factor of $a$ $a$ units.
If the values of $a$ $a$ are negative, this will result in the graph reflecting vertically across the x-axis.

A horizontal stretch is the stretching of a function on the y-axis.
If $| b | < 1$ $|b|<1$ , then the graph is stretched horizontally by a factor of $b$ $b$ units.
If the values of $b$ $b$ are negative, this will result in the graph reflecting horizontally across the y-axis.

For example:
$y = 2 f ((\frac{1}{2}) x - h)) + k$ $y=2f((1/2)x-h))+k$
$a = 2$ $a=2$

$b = \frac{1}{2}$ $b=1/2$

To vertically stretch we use this formula:
$y^{1} = a y$ $y^1=ay$
$y^{1} = 2 y$ $y^1=2y$ So, the vertical stretch would be by a factor of 2.

To horizontally stretch we use this formula:
$x^{1} = \frac{x}{b}$ $x^1=x/b$

$x^{1} = \frac{x}{\frac{1}{2}}$ $x^1=x/(1/2)$

$x^{1} = 2 x$ $x^1=2x$ So, the horizontal stretch would be by a factor of 2 as well.

Extras:
If $| a | < 1$ $|a|<1$ , this results in a vertical compression.
If $| b | > 1$ $|b|>1$ , this results in a horizontal compression.

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How do I find the stretches of a transformed function?

Do I look for the x and y intercepts and the invariant points?

1 Answer

Explanation:

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