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Dominik [7]
3 years ago
15

Which values are with in the range of the piecewise defined function?

Mathematics
2 answers:
guapka [62]3 years ago
8 0
<h2>Answer:</h2>

The range of the piecewise defined function is:

                  y= -6 , y= -4 , y= -3 , y=0

<h2>Step-by-step explanation:</h2>

The piecewise function is defined by:

f(x)  =    2x+2   when  x < -3

              x       when  x = -3

  and  -x-2      when  x > -3

  • when x < -3

Then the graph of the function is a strictly increasing function and is a line with a slope of 2.

The function increases continuously from -∞ to -4

i.e. it takes all the value in the interval (-∞,-4)

There is a open circle at (-3,-4)

  • Also, at x= -3 the value of function is : -3
  • For x > -3

The graph of the function f(x) is strictly decreasing .

Since the graph is a line with slope -1.

Also, there is a open circle at (-3,1)

and the function starts decreasing continuously and will take all the values strictly less than 1.

i.e. the range for x > -3 is:  (-∞,1)

The range of the whole function f(x) is:

                            (-∞,1)

zepelin [54]3 years ago
4 0

Answer:

y = -6; -3;  0

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)  = 2x+2  , x < -3

f(x) = x, x = -3

f(x) = - x -2 , x > -3

From the graph, we can see that the values are

y = -6; -3;  0

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we know that

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6 0
3 years ago
A study was designed to investigate the effects of two​ variables, (1) A​ student's level of mathematical anxiety and​ (2) teach
Mashcka [7]

Answer:

P(X>400)=P(\frac{X-\mu}{\sigma}>\frac{400-\mu}{\sigma})=P(Z>\frac{400-440}{20})=P(z>-2)

And we can find this probability using the complement rule:

P(z>-2)=1-P(z

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(z>-2)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(440,20)  

Where \mu=440 and \sigma=20

We are interested on this probability

P(X>440)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>400)=P(\frac{X-\mu}{\sigma}>\frac{400-\mu}{\sigma})=P(Z>\frac{400-440}{20})=P(z>-2)

And we can find this probability using the complement rule:

P(z>-2)=1-P(z

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(z>-2)=1-P(z

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Answer:

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Step-by-step explanation:

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G(t) = 3t+ 4; Find g(−3)
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Answer:

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Step-by-step explanation:

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