Transformations in Function Notation

Translation 2 units left

Translation 2 units right

Reflection across the x-axis

Reflection across the y-axis

$f\left(x\right)+2$

$f\left(x\right)-2$

$f\left(x+2\right)$

$f\left(x-2\right)$

Reflection across the x-axis and translation 1 unit up

Reflection across the y-axis and translation 1 unit up

Translation 1 unit right and 3 units up

Translation 3 units right and 1 unit up

$f\left(x-3\right)+1$

$f\left(x+1\right)+3$

$f\left(x-1\right)+3$

The x-values stay the same while the y-values flip signs

The x-values flip signs while the y-values stay the same

Both the x-values and the y-values flip signs

Both the x-values and the y-values stay the same

$f\left(x\right)$

$f\left(-x\right)$

$-f\left(x\right)$

$-f\left(-x\right)$

It would move to the right

It would look the same

It would turn upside down

It would get smaller