No this doesn't mean that multiplying f(x) by 1/3 and subtracting 4 from f(x) transform the graph in the same way
Step-by-step explanation:
Let us revise some transformation:
- A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis, if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
∵ f(x) = 6 - 3x
∵ [tex]\frac{1}{3}[/tex] f(x) means we multiply y by a factor [tex]\frac{1}{3}[/tex]
- The graph of f(x) is compressed by factor [tex]\frac{1}{3}[/tex]
∴ [tex]\frac{1}{3}[/tex] f(x) = [tex]\frac{1}{3}[/tex] (6 - 3x)
∴ [tex]\frac{1}{3}[/tex] f(x) = [tex]\frac{1}{3}[/tex] (6) - [tex]\frac{1}{3}[/tex] (3x)
∴ [tex]\frac{1}{3}[/tex] f(x) = 2 - x
∵ f(x) - 4 means the graph of f(x) is translated 4 units down
- That means subtract 4 from y
∴ f(x) - 4 = (6 - 3x) - 4
- Add like terms
∴ f(x) - 4 = (6 - 4) - 3x
∴ f(x) - 4 = 2 - 3x
The two new graphs have same y-intercept but different slopes and the first graph is the image of the graph of f(x) by vertical compression with factor 1/3 and the second graph is the image of the graph of f(x) by translation 4 units down
Look to the attached graph for more understand
No this doesn't mean that multiplying f(x) by 1/3 and subtracting 4 from f(x) transform the graph in the same way
Learn more:
You can learn more about transformation in
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