Question

Aidan observes that if f(x) = 6 − 3x, then the graphs of 13f(x) and f(x) − 4 both have a y-intercept of 2.

Answer 1

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

∵ $\frac{1}{3}$ f(x) means we multiply y by a factor $\frac{1}{3}$

- The graph of f(x) is compressed by factor $\frac{1}{3}$

∴ $\frac{1}{3}$ f(x) = $\frac{1}{3}$ (6 - 3x)

∴ $\frac{1}{3}$ f(x) = $\frac{1}{3}$ (6) - $\frac{1}{3}$ (3x)

∴ $\frac{1}{3}$ 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

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