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I need specific help in reading a piecewise function and writing the domain and the range in interval and set builder notation. Thank you!

Question

I need specific help in reading a piecewise function and writing the domain and the range in interval and set builder notation. Thank you!

check_circleAnswer
Step 1

We first begin with the definition of piecewise defined function.

A piecewise defined function is a function defined by two or more equations i.e. "pieces", each of which lies in different part of the domain. 

Their "pieces" may be all linear, or a combination of functional forms (such as constant, linear, quadratic, cubic, square root, cube root, exponential, etc.)

Step 2

For example:

x2;
f(x)x 2
x 0
0 x3
4;
x > 3
help_outline

Image Transcriptionclose

x2; f(x)x 2 x 0 0 x3 4; x > 3

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Step 3

For Domain and Range:

It's very important to watch your greater/less than or equal to signs, as two points on the same domain...

For the first function, y x2 is a simple parabola, and so the origin, (0,0) and it is extended
indefinitely in both directions. However, the x-values for the given function less than 0, so we
will only draw the left half of the graph, without including 0
help_outline

Image Transcriptionclose

For the first function, y x2 is a simple parabola, and so the origin, (0,0) and it is extended indefinitely in both directions. However, the x-values for the given function less than 0, so we will only draw the left half of the graph, without including 0

fullscreen

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