Question

Suppose f(x) = x2 and g(x) = (4x)2. Which statement best compares the graph of g(x) with the graph of f(x)?

A. The graph of g(x) is horizontally stretched by a factor of 4.

B. The graph of g(x) is shifted 4 units to the right.

C. The graph of g(x) is vertically stretched by a factor of 4.

D. The graph of g(x) is horizontally compressed by a factor of 4.

Answer 1

Answer:

Option C

Step-by-step explanation:

Given: Functions  $f(x) = x^2$  and  $g(x)=(4x)^2$

Now, if we compare the both equation we get,

$g(x) = 4f(x)$  as  $g(x) = 4(4x^2)=16x^2=(4x)^2=f(x)$

This means that the value of g(x) is 4 times the value of f(x). So the graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.

The graph shown below confirms the conclusion.

Therefore, Option C is correct.

The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.

Answer 2

The statement that best compares the graph of g(x) with the graph of f(x) is (c) the graph of g(x) is vertically stretched by a factor of 4.

The functions are given as:

$f(x) = x^2$

$g(x) = (4x)^2$

Expand the function g(x)

$g(x) = 16x^2$

Substitute f(x) for x^2

$g(x) = 16f(x)$

This gives

$g(x) = 4 * 4f(x)$

$g(x) = f(4x)$

The above means that: f(x) is vertically stretched by a factor of 4 to get g(x)

Hence, the true statement is (c)

Read more about function transformation at:

https://brainly.com/question/1548871