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Please Answer!!! how do the graphs of (x) = x^2 and g (x)= 3/4 x^2? relate?
a. the graph of g(x) is the graph of f(x) compressed horizontally by a factor of 3/4
b. the graph of g(x) is the graph of f(x) compressed vertically by a factor of 3/4
c. the graph of g(x) is the graph of f(x) compressed vertically by a factor of 4/3
d. the graph of g(x) is the graph of f(x) compressed horizontally by a factor of 4/3

Respuesta :

C bc it has the most sense

Answer:

The correct option is B.

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

[tex]g(x)=\frac{3}{4}x^2[/tex]

It can be written as

[tex]g(x)=\frac{3}{4}f(x)[/tex]                  .... (1)

The vertical stretch and compression is defined as

[tex]g(x)=kf(x)[/tex]                  .... (2)

If k>1, then it represents vertical stretch by factor a.

If 0<k<1, then it represents vertical compression by factor a.

From (1) and (2), we get

[tex]k=\frac{3}{4}[/tex]

Since k<1, therefore he graph of g(x) is the graph of f(x) compressed vertically by a factor of 3/4.

Hence the correct option is B.

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