Question

Suppose that f(x) = x2 and g(x) = 2/5 x2 Which statement best compares the
graph of g(x) with the graph of f(x)?
O
A. The graph of g(x) is the graph of f(x) compressed vertically.
O
B. The graph of g(x) is the graph of f(x) compressed vertically and
flipped over the x-axis.
O
C. The graph of g(x) is the graph of f(x) stretched vertically and
flipped over the x-axis.
O
D. The graph of g(x) is the graph of f(x) stretched vertically.

Answer 1

The statement best compares the  graph of g(x) with the graph of f(x) is The graph of g(x) is the graph of f(x) stretched vertically.

Option: D.

Step-by-step explanation:

The given equations are f(x) = $x^2$ and g(x) = $(\frac{2}{5})x^2.$

The f(x) and g(x) will be the value in the y-axis (vertical).

∴ The g(x) is dilated with the factor $\frac{2}{5}$ from f(x). That is f(x) is actually reduced.

When the x value is applied in the equations the value respective y values obtained for both equations.

The values of g(x) is comparatively lesser than f(x).

For example,

if x= -5,

then f(x)=25 and g(x)=10.

I.e) for each points there is a vertical difference. (refer the graph uploaded below).

Thus the graph of g(x) is the graph of f(x) stretched in the x-axis vertically.