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Goshia [24]
3 years ago
11

Graph the piecewise-defined function.

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
7 0

Answer:

We are asked to find which graph represents the graph of the piecewise-defined function g(x) given as:

g(x)= x^2-4   ;  if  x < -1

            1       ;   if  -1≤ x ≤ 1

   and   x^2+4   ; if x>1

i.e. in the region (-∞,-1) we will get a graph of a quadratic function x^2-4.

in the region [-1,1] we will get a straight line y=1.

and the region (1,∞) again we will get a graph of a quadratic function x^2+4.

Also the graph of the function is discontinuous at 1 and -1.

since the limit of the function at x=-1 and at x=1 does not exist.

As at x=-1.

Left hand limit= -3   (x^2-4; at x=-1 gives -3)

and right hand limit =1.

Whereas at x=1.

left hand limit=1

and right hand limit=5    ( x^2+4=1+4 )

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ira [324]

Answer:

<h3><u>Mean</u></h3>

<u />

\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}

\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10

\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10

<h3><u>Standard Deviation</u></h3>

\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}

\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}

\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}

<h3><u>Summary</u></h3>

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The <u>mean</u> scores are the <u>same</u>.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.

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Answer:

I have attached the work to your problem.

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