Question

the graph of f(x), shown below, has the same shape as the graph of G(x)=x^4-x^2, which contains the point (0,0) Which of the following is the equation of F(x)

Answer 1

Answer: Option B

`F (x) = x ^ 4-x ^ 2 + 4`

Explanation:

We have the function
`G (x) = x ^ 4-x ^ 2` and we know that it contains the point (0,0). That is, it cuts the y axis and y = 0

Then the graph of F(x) is shown in the image and we know that it is a transformation of F(x).

The function F(x) cuts the y axis and y = 4.

For this reason we can conclude that the function F(x) is the function G(x) displaced 4 units upwards.

The transformation that shifts the graph of a function k units upwards is:

`F (x) = G (x) + k`

Where
`k> 0`.

In this case k = 4. Therefore:

`F (x) = G (x) +4\\\\F (x) = x ^ 4-x ^ 2 + 4`

The answer is Option B