The graph of y=1/2^3√x-4 can be obtained from the graph y=^3√x by which transformations
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The graph of y=1/2^3√x-4 can be obtained from the graph y=^3√x by which transformations

[From: ] [author: ] [Date: 12-05-21] [Hit: ]
The first question implies that only the second interpretation makes sense.Now, transforming a function of the form y = f(x) to y = f(x - a) moves the graph a units to the right. So, replacing x with x - 4 moves the graph of y = (1/2)x^(1/3) 4 units to the right to get y = (1/2)(x - 4)^(1/3), and the answer is (b).......
What is the horizontal shift?
(a) 2 units to the left
(b) 4 units to the right
(c) 2 units to the right
(d) 4 units to the left

By what factor must the graph of y=^3√x be stretched or shrunk?
(a) shrink by a factor of 1/2
(b) stretch by a factor of 2
(c) shrink by a factor of 2
(d) stretch by a factor of 1/2

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Your notation is quite confusing. From context, you mean either:
y = x^(1/3) and y = (1/2)x^(1/3) - 4 OR y = x^(1/3) and y = (1/2)(x - 4)^(1/3).

The first question implies that only the second interpretation makes sense.

Now, transforming a function of the form y = f(x) to y = f(x - a) moves the graph a units to the right. So, replacing x with x - 4 moves the graph of y = (1/2)x^(1/3) 4 units to the right to get y = (1/2)(x - 4)^(1/3), and the answer is (b).

For the second question, notice that 1/2 < 1, so the graph is compressed. Since all of the y-coordinates are halved, the graph shrinks by a factor of 2 and the answer is (c).

I hope this helps!
1
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