The Tough One

There is one combination of transformations that gets tricky.

Combining a horizontal translation and a horizontal (which is y-axis) reflection.

This combination is an issue because both of them are in the horizontal direction and the changes in the equations are therefore linked.

Imagine this transformation.

From looking at the transformed equation, what do the two transformation appear to be?

(scroll down when you've got them)

Most likely you identified a y-axis reflection and a horizontal shift right 2 units.

Now, because of the y-axis reflection (horizontal flip) there is a negative sign in front of the variable

so imagine if someone chose to factor out that negative sign as shown here.

Now, what do the two transformations appear to be?

There should still be a y-axis reflection, however, now the horizontal shift is left 2 units.

On your calculator, graph y=abs(-x-2) and determine which set of transformations is the correct one.

*abs() is the way to type absolute value into most graphing utilities including TI-calculators.