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### Course: Algebra 1>Unit 10

Lesson 1: Graphs of absolute value functions

# Scaling & reflecting absolute value functions: equation

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 a description of the transformation performed on y=|x|.

## Want to join the conversation?

• Is there any way to tilt or rotate the function? I.e rotate the function by say 45 degrees.
• yes, there is a way, but it requires knowledge of things called parametric equations, trigonometry, and also linear algebra. you'll encounter these later on in your math classes (assuming you take them past grade 10)
• The 7 is the slope, right?
• Sort of, but not quite. The function would be f(x) = - 7 | x|. For x ≤ 0, the slope would be 7 with a y intercept of (0,0). For x ≥ 0, the slope would be -7 with a y intercept of (0,0). So you have to consider which part of the graph you are talking about.
• what scaled even mean?
• "Scaled" means the graph rises faster or slower than the standard function of y=|x|. For example, y=2|x| rises twice as fast so the V-shape will be narrower.
Hope this helps.
• can functions have graphs in a v shape and not be absolute value functions? Like an assymetrical v shape?
• Yes, piecewise functions have a different calculation that determines the shape of each piece.
• Can u flip it on the y axis as well?
• Yes you can flip it on y axis if the points are on the left or right side of the axis.
• Hi, is -7|x| equal to -|7x|? Can you write -7|x| as -|7x|?
• Yes, those are equivalent expressions.
• Is there any way to tilt or rotate the function? I.e rotate the function by say 45 degrees.
• I don't think so. Wouldn't the function then change, because of each input having only one output?
• how did he graph that y=-7 absolute value of x
• Read the problem at the top. If asks for the graph of y=|x| reflected across the x-axis and then scaled vertically by a factor of 7. It also asks for the equation for that graph.
• why does the 7 on the x axis start near 1
• Sal has 3 graphs:
y=|x|
y=-|x|
y=-7|x|

I also don't see any point on a graph that is (7,1). If x=7, here are the points that would be on each graph.
The 1st graph y=|x| would have a point (7,7)
The 2nd graph y=-|x| would have a point (7,-7)
The 3rd graph y=-7|x| would have a point (7,-49)

I don't know if this helps. If you clarify your question, may be I can help further.