Question

The graph of f(x) = x2 is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?
A) graph F
B) graph G
C) graph H
D) graph J

Answer 1

Answer:

Graph J

Step-by-step explanation:

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x) = 2x²

Now, for x = 0, f(x) = 0 and h(x) = 0

Therefore, both the graphs passes trough the origin.

Now, for x = 1, f(x) = 1 and h(x) = 2

Therefore, f(1) < h(1)

Hence, the graph J represents the correct graph of f(x) and h(x). (Answer)

Answer 2

The graph that best represents the given functions f and h is:

Graph J. Thus, we have

Option D) graph J  is the graph which best represents f and h.

Given that:

• $f(x) = x^2$

• $h(x) = 2\times f(x)$

Explanation:

Since for each value of f(x), the corresponding value of h(x) is doubled.

Whenever the value of h(x) is doubled, it is mapped higher than the mapped value of f(x). It is because the y axis where the outputs are mapped is vertical and its magnitude rises upwards.

Thus, the fourth graph where h(x) is mapping higher than that of f(x) represents both functions f and h in the best manner.

Thus, Option D) graph J  is the graph which best represents f and h.

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