Question

Which of the following are true about the graph of f(x)=-4x^2?
Select all that apply.
A)The domain is {x|x is a real number}
B)The range of f is (-infinity, -4].
C)f is decreasing over the interval (-infinity, infinity).
D)The point (0,0) is a maximum.
E)There are two x-intercepts.​

Answer 1

• The parabola is a flat curve that is Spiegler and about U-shaped.
• It corresponds to numerous superficial mathematical descriptions, all of which can be shown to define exactly the same curves.
• A parabola is described by the point (focus) as well as an axis (the directrix).

Given:

$\to \bold{ f(x)=-4x^2}\\\\Let\\\\\to \bold{y=f(x)}\\\\\therefore \ \ \\\to \bold{y=-4x^2}\\\\\to \bold{ x^2=-\frc{1}{4}y}$

Equation of parabola:

$\to \bold{\text{domain=real number}}\\\\\to \bold{\text{range=}( \infty ,0)}}$

is decreasing over $\bold{(0, \infty)}$and increasing over $\bold{(-\infty,0)}$.

$\to \bold{(0,0)}$ is a maximum these are only one x-intercept at $\bold{ x=0}$  

Therefore, the final answer "Option A and Option D".

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Answer 2

A function can be represented as a graph which shows its characteristics

The true statements about the function f(x) = -4·x² are;

• The domain is {x | x is a real number}

• The point (0, 0) is a maximum

The reason the above option are correct as follows:

The given function is presented as follows;

f(x) = -4·x²

Given that the operation in the function is the raising of the power of x to two, followed by multiplication by '-4', which are operations defined for all real numbers, the function can take all real numbers as input

Therefore;

• The domain is {x | x is a real number}

The 'x²' in the function f(x) always gives a positive value, therefore, -4·x² is always negative, except for the point x = 0, where, -4 × 0² = 0 = f(0)

Therefore, f(x) = -4·x² is 0, when x = 0, which is the only nonnegative value and therefore, the maximum point, and the only x and y intercept

Therefore;

• The point (0, 0) is a maximum

The function is increasing in the domain (-∞, 0]

The range of the function is (-∞, 0]

Therefore, two true statements are;

A) The domain is {x | x is a real number}

D) The point (0, 0) is a maximum

Learn more about properties of the graph of a function here:

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