Mathematics, 28.06.2019 04:40, 1Angel2Got3Brains

Which of the following piecewise functions is graphed above?

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answered: laylalucifer

Hello!

The answer is:

The piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

$8; x\leq -1\\\\x^{2} -4x+1;-1$

Why?

To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).

From the graph, we know that we need the following functions:

- A horizontal line, which exists from -∞ to -1, givind as input 8.

The function will be:

y=8

Then, the piecewise function it will be:

$8; x\leq -1$

- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)

The function will be:

$y=x^{2}-4x+1$

Finding the y-intercept, we have:

$y=0^{2}-4*80)+1$

y=1

Finding the vertex of the parabola, we have:

$x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2$

$y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1$

$y_{vertex}=2^{2}-4*2+1=4-8+1=-3$

The vertex of the parabola is located at the point (2,-3).

Then, for the piecewise function it will be:

$x^{2} -4x+1;-1$

- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.

The function will be:

y=-x+1

Proving that it's the correct equation by evaluating "x" equal to 5, we have:

y=-5+1

y=-4

It proves that the equation is correct.

Then, for the piecewise function it will be:

$-x+1\geq 5$

Hence, we have that the piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

$8; x\leq -1\\\\x^{2} -4x+1;-1$

Have a nice day!

answered: Guest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

answered: Guest

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