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Graph the following equation. y = 2(f(x))
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High School Teacher
If you are given f(x) and you are asked to graph y=2(f(x)):
Note that the type of graph will not change. So a line remains a line, a parabola remains a parabola, etc... Multiplying by 2 is a dilation (stretch) of factor 2.
You can build a table with the following headings: x ; f(x) ; 2f(x) and plot the points.
Alternatively, you can graph y=f(x) and then take each y-value and double it to form the graph of y=2f(x).
For example, if `y=x^2` then you have, among others, the points (-2,4),(-1,1),(0,0),(1,1),(2,4). The function `y=2f(x)=2x^2` has the following points: (-2,8),(-1,2),(0,0),(1,2),(2,8)
Posted by embizze on September 22, 2013 at 2:06 AM (Answer #1)
What Embizze has is absolutely correct. I wanted to add, it's a dilation as in, it gets stretched from the x axis. So, for example, the graph of y = 3x:
It would be the black line. But, then, multiply f(x) by 2, so:
y = 3x --> y = 2*3x = 6x
The new graph becomes:
The new graph is in red. As the perspective is, one talks of how each point gets moved away from the x axis further. It goes up above the x axis and down below the x axis. All the same with the quadratic curve Embizze showed.
Good luck, Kristen. I hope this helps.
Posted by steveschoen on September 22, 2013 at 5:26 AM (Answer #2)
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