graphing an absolute value function

[rayne1993]

ok so we started with parabolas, we work A LOT with graphs, example problem would be:

graph y=|-1/4x-1|; i know that the -1 means to move to the right 1 time, but what does the -1/4 tell you to do???

i don't think you flip the parent function unless the negative is outside the absolute value sign, right? :?

 

[lookagain]

ok so we started with parabolas, we work A LOT with graphs, example problem would be:

graph y=|-1/4x-1|; i know that the -1 means to move to the right 1 time, but what does the -1/4 tell you to do???

i don't think you flip the parent function unless the negative is outside the absolute value sign, right? :?

\(\displaystyle y = \left|\frac{-1}{4}x - 1\right|\)


Factor out a \(\displaystyle 1/4:\)

\(\displaystyle y = \frac{1}{4}\left|-x - 4\right|\)


This can become

\(\displaystyle y = \frac{1}{4}\left|x + 4\right|\)


There is a horizontal shift of 4 units to the left and a compression by a factor of 1/4 done to the parent function.

For example, the vertex in the parent function at (0,0) gets moved to (-4, 0), and the points
(-4, 4) and (4, 4) get translated to (-8, 1) and (0, 1), respectively.