How do you translate a graph up or down?

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How do you translate a graph up or down?

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Answer 1 · 2014-09-22T05:35:05

You can translate any function, $y = f (x)$ $y=f(x)$ using:

$y = f (x - h) + k$ $y=f(x-h)+k$ or
$y - k = f (x - h)$ $y-k=f(x-h)$

If $h$ $h$ is positive, the graph will translate to the right.
If $h$ $h$ is negative, the graph will translate to the left.
If $k$ $k$ is positive, the graph will translate up.
If $k$ $k$ is negative, the graph will translate down.

Here is an example:

$f (x) = x^{2} + 2 x$ $f(x)=x^2+2x$

If we want to translate this up 4 units, then we have:

$y = f (x) + 4$ $y=f(x)+4$
$y = x^{2} + 2 x + 4$ $y=x^2+2x+4$

If we have a different example:

$f (x) = \frac{1}{x}$ $f(x)=1/x$
$y = f (x) + 4$ $y=f(x)+4$
$y = \frac{1}{x} + 4$ $y=1/x+4$

It still works!

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How do you translate a graph up or down?

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