Question

uiz Copy 1 Which of the following are true about the graph of f(x) = -4x2? Select all that apply A. The domain is x B. The range of f is (-0, -4]. C. fis decreasing over the interval (-00,00) D. The point(0, 0) is a maximum. E There are two x-intercepts.

Answer 1

A, D and E

Step-by-step explanation

The function we are given is:

`\text{y = -4x}^2`

OPTION A

It is true that the domain of the function is every real value.

This is because there is no value of x that will not yield a valid value of y.

So, it it true.

OPTION B

This is not true because the maximum value of the function is 0 and there is no lowest value of y as y is continuous over the values of x.

So, it is not true.

OPTION C

This is not true.

This is because x is actually only decreasing over the interval:

`(0,\text{ }\infty)`

It actually increases over the interval:

`(-\infty,\text{ 0)}`

OPTION D

It is true that the point (0, 0) is the maximum point of the function.

When x is 0, f(x) is 0 but any other value of x gives a negative value of f(x). So, it is true.

OPTION E

The function is a quadratic function.

A quadratic function has two roots and hence it touches the x axis at two points.

So, it is true.

The correct options are A, D and E.