When we multiply a function by a constant, the graph either stretches out or compresses. Transforming a function in this way is called scaling.
To illustrate, consider the graph of shown below.
The following table lists four sets of points. The set of points in the left-hand column correspond to the graph of and the set on the right-hand side corresponds to
For each point on the graph of there is a point on the graph of with the same -value and double the -value.
Now that we have four points on the graph of let's plot the full graph.
We say that the graph of is the graph of vertically stretched by a scale factor of
We can also say that the graph of is the graph of stretched by a factor of parallel to the -axis.
The graph of is shown below. Sketch the graph of
To graph the function we take the graph of and stretch it by factor of parallel to the -axis. This has the effect of multiplying the -coordinates of all points on by
The resulting graph is the solid blue curve shown below.
The graph of $y=f(x)$ is shown above. Which of the following is the graph of $y=2f(x)?$
(Note: Figures not drawn to scale)
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The graph of $y=f(x)$ is shown above. Which of the following is the graph of $y=3f(x)?$
(Note: Figures not drawn to scale)
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The graph of is shown above. Sketch the graph of
To graph the function we take the graph of and compress it by factor of parallel to the -axis. This has the effect of dividing the -coordinates of all points on by
The resulting graph is the solid blue curve shown below.
The graph of $y=f(x)$ is shown above. Which of the following is the graph of $y=\dfrac{1}{2}f(x)?$
(Note: Figures not drawn to scale)
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The graph of $y=f(x)$ is shown above. Which of the following is the graph of $y=\dfrac{1}{3}f(x) ?$
(Note: Figures not drawn to scale)
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The point with coordinates lies on the curve Find a point that must lie on the graph of
The function represents a stretch of the function by a factor of parallel to the -axis. This has the effect of multiplying the -coordinates of all points on by
Therefore, the point on is mapped to the point and this point must lie on the graph of
The point $P$ with coordinates $(8, 12)$ lies on the curve $y =f(x).$ Which of the following points must lie on $y = 2f(x)?$
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$(8, 6)$ |
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$(16, 24)$ |
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$(8, 12)$ |
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$(16, 12)$ |
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$(8, 24)$ |
The point $P$ with coordinates $(1, 8)$ lies on the curve $y =4f(x).$ Which of the following points must lie on $y = f(x)?$
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$(1, 8)$ |
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$\left(\dfrac{1}{4}, 2\right)$ |
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$(1, 32)$ |
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$(1, 2)$ |
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$(4, 8)$ |
If the point $P$ with coordinates $(-16, 40)$ lies on the curve $y=f(x),$ then the point $Q$ must lie on $y=\dfrac{1}{8}f(x).$ What are the coordinates of $Q?$
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