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nikitadnepr [17]
3 years ago
8

The graph of the function f(x)= -(x+3)(x-1) is shown below. What is true about the domain and range of the function?

Mathematics
1 answer:
sertanlavr [38]3 years ago
8 0

Answer:

The domain is all real numbers, and the range is all real

numbers less than or equal to 4.

Step-by-step explanation:

The domain of a function f(x) is the set of all values for which the function is defined

We are given f(x)= -(x+3)(x-1)

f(x) is defined for all real values of x since there are no restrictions on the value of x

So,The domain of the function is all real numbers

Range of the function is the set of all values that f takes.

So, Range of given function is all real numbers less than or equal to 4.

Hence The domain is all real numbers, and the range is all real  numbers less than or equal to 4.

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worty [1.4K]
The full range is -\pi (length 2L=2\pi), so the half range is L=\pi. The half range sine series would then be given by

f(x)=\displaystyle\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L=\sum_{n\ge1}b_n\sin nx

where

b_n=\displaystyle\frac2L\int_0^Lf(x)\sin\dfrac{n\pi x}L\,\mathrm dx=\frac2\pi\int_0^\pi(\pi-x)\sin nx\,\mathrm dx

Essentially, this is the same as finding the Fourier series for the function

\begin{cases}g(x)=\begin{cases}\pi-x&\text{for }0

Integrating by parts yields

b_n=\dfrac2\pi\left(\dfrac\pi n-\dfrac{\sin n\pi}{n^2}\right)=\dfrac2n

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..........................

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