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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: 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 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.
• What if we scaled horizontally by a factor of 7?
• Scaling horizontally by a factor of 7 means that instead of 𝑥 we get 7𝑥.
So, scaling 𝑦 = −|𝑥| horizontally gives us 𝑦 = −|7𝑥|.
• So scaling by a factor of 7 is different from just moving the function up by 7 like in the previous video?
• Yes. Scaling is sort of like stretching the graph vertically, where as moving the function up preserves the shape. If the function is x, scaling it would produce 7x, where as moving it upwards produces x+7. If you graph both functions, you can clearly see the difference.
(1 vote)
• In the previous video, we added 7 to the equation. Now we're multiplying. by 7. Why don't we just add 7 like the other video?
• When we graphed linear equations, we saw that y = x+7 is not the same as y = 7x.

y = 7x means for every x, y is 7 times as large. This produces a very steep line.

The same thing applies here. "Scaled vertically" is a fancy way of saying the line looks steeper (i.e. stretched along the y-axis). y = 7|x| means for every x, y is 7 times as large.

On the other hand, y = |x| + 7 means you add seven to each x to get y.
(1 vote)
• Why do we call it "vertical" scaling? What's the difference between scaling such graphs vertically and horizontally?
• sal says, "hopefully this is familiar. You've seen the graph of y is equal to absolute value of x before."

I have not. This is not familiar. Would someone please provide a link to where I need to go on Khan? Thank you!
(1 vote)
• Confused. Since x is absolute value it is always positive? How can the graph go to the left of zero?
(1 vote)
• The value of "x" doesn't need to be positive. The absolute value turns "x" into a positive. For example, if x=-3, then |-3|=+3. The absolute value is impacting the value of Y, not X.

Hope this helps.