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## Get ready for Algebra 2

### Course: Get ready for Algebra 2>Unit 3

Lesson 7: Graphs of absolute value functions

# Scaling & reflecting absolute value functions: graph

The graph of y=k|x| is the graph of y=|x| scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of an absolute value function from its graph.

## Want to join the conversation?

• How would you stretch it?
• You always stretch any function by adding an a in front of highest power of the function, so with the absolute value parent function, f(x) = | x |, adding a number greater than 1 causes a vertical stretch such as f(x) = 2 | x |, and between 0 and 1 is a vertical compression such as f(x) = 1/2 | x |
• Would you recommend stretching the function or flipping the function first?
• It's irrelevant and completely up to your preference.
• ok is thisd real man?
(1 vote)
• Why not -5 times as it touch both lines?
(1 vote)
• So, basically, y= -4 lxl is the equation. Would you say, in general of course, that -4, when outside the abs. value symbol, is kind of like the slope (-4/1)?
(1 vote)
• Kind of...
A simple absolute value function like you have will create a V-shaped graph. The -4 does 2 things to the V.
1) It makes the V narrower (like having a steeper slope
2) The negative sign flips the V upside down.

Hope this helps.
(1 vote)
• What is the difference between a horizontal stretch and a vertical stretch? Don't they still look the same??
(1 vote)
• No, stretching is like pulling either up (vertical) or out (horizontal). A vertical compression pushes things toward the x axis, so a vertical compression will look the same as a horizontal stretch, and a vertical stretch will look like a horizontal compression.
(1 vote)
• I am confused about scaling using the factor. I understand about shifting to the left or to the right, and going up or down on the y axis, but I don't understand how you determine to stretch or compress the graph with the factor. For example, f(x) = 2|x+3| +2, please explain how to scale it by 2. The |x+3| means move the whole graph to the left by 3; the +2 means move the graph up by 2 on the y axis. But how do I scale it to a factor of 2? Thank you
(1 vote)
• Hunter,

Have you graphed linear equations before? If so, you should be familiar with having a number in front of x.

E.g. y = 2x. For every x, y is twice as much. The line becomes quite steep when you have a whole number; a fraction causes the line to be less steep.

Same thing here. y = 2|x| has a compressed V-shape; y = 1/2|x| is stretched out.

In your equation, start off with y = |x|. Before doing the shift left and shift up stuff, draw y = 2|x|. You will see a compressed V-shape compared to y = |x|. Then apply the other transformations.
• If it is across the x axis, how could one change the y- intercept if the slope is not determined?
(1 vote)
• While I am not sure exactly what you are asking, the problem shows the vertex of the absolute value function at the origin. If the vertex is anywhere else but the vertex, then the y-intercept would have to be the additive inverse of the original y-intercept. On a graph, it should not be too difficult to determine the slope. Is this sort of what you are asking?
• whats would you do if you had a fraction?
(1 vote)
• A fraction causes the V-shape of the graph to stretch out (whole number, as in this video, causes the graph to squeeze).

Let's compare y = |x| and 1/2|x|

|x|: When x=1, y=1; when x=-1, y=1

1/2|x|: When x=1, y=1/2; when x=-1, y=1/2

If you have graph paper, try drawing these graphs and see what the fraction does.