Suppose f(x)=x^2 and g(x)=5x^2. which statement best compares the graph of g(x) with the graph of f(x)? a) the graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5 b) the graph of g(x) is the graph of f(x) vertically compressed by a factor of 5 c) the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5 d) the graph of g(x) is the graph of f(x) shifted 5 units right

C

Step-by-step explanation:

A vertical stretch of a function means the output values have changed by a factor or multiplication by a number. Recall, a quadratic function has the basic form .

Our function g(x) is meaning any value out of f(x) will be multiplied by 5 and the values increase by a factor of 5. This is a vertical stretch.

The statement that reads "the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5" is correct.

Option c - The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Step-by-step explanation:

Given : Suppose and

To find : Which statement best compares the graph of g(x) with the graph of f(x)?

Solution :

and

The graph of g(x) is multiplied by 5 of f(x) shows the vertical stretch.

Vertically stretch :

When y=f(x) → y=bf(x) i.e, the graph is b unit vertically stretched and b>1.

In the graph of → i.e, 5 unit is multiplied.

Therefore, Option c is correct i.e, the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

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Step-by-step explanation: