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3 years ago

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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Step-by-step explanation:

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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:

$X \sim N(440,20)$