Question

Suppose that g(x) = f(x) + 3. which statement best compares the graph of g(x) with the graph of f(x)?

A. the graph of g(x) is shifted 3 units to the right
B. the graph of g(x) is shifted 3 units down.
C. the graph of g(x) is shifted 3 units up.
D. the graph of g(x) is vertically stretched by a factor of 3.

Answer 1

C. the graph of g(x) is shifted 3 units up

Explanation:

Given: g(x) = f(x) + 3

Here the graph of g(x) = the graph of f(x) + 3, where 3 represents the vertical shift.

Since it is 3, so the graph moves 3 units up.

Answer: C. the graph of g(x) is shifted 3 units up.

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Answer 2

C. the graph of g(x) is shifted 3 units up.

Explanation:

The statement that compares the graph of g(x) with the graph of f(x) is that the graph of g(x) is shifted 3 units up.

If we have the equation:

G(x) = F(x) + 3

Then, the graph of G(x) will be composed of points 3 units above the graph of F(x).

Conversely, the difference between F(x) and G(x) at any particular value of x will always be 3.