Question

The graph of f(x), shown below has the same shape as the graph has the same shape as the graph of g(x)=x^4-X^2 which contains the (0,0) which of the following is the equation of f(x)

Answer 1

A. F(x) = x^4 - x^2 + 4

B. F(x) = 4 - X^4 - X^4 - X^2

C. F(x) = x^4 - x^2

D. F(x) = x^4 - x^2 - 4

The answer is A

Answer 2

First of all it is always a good idea to graph a question like this one. Here are the three graphs

y = x^4 - x^2 Color: Red This is the base graph
y = x^4 - x^2 - 4 Color Blue This has - 4 added to it.
y = x^4 - x^2 + 4 Color Green This has 4 added to the base graph

Which one is correct? The red and blue one are not. The graph you want is plotted upward from the base graph. The base graph (red nothing added to it) is not right because it has points on the x axis. The graph you want does not.

The same is true of the blue graph. It cuts the x axis. That only leaves the green one.

Answer: C