Mathematics, 31.08.2019 07:30 dbanks701

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.

Answers: 1

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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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Which of the following are true about the graph of f(x)=-4x^2? select all that apply.a)the domain is

Answer from: kaseyvn03

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

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Which of the following are true about the graph of f(x)=-4x^2?
select all that apply.
a)t...

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