Question

Can someone please identify and correct the error that I made in graphing the f(x)= -3 if -5<=x<-2?Please show your work on how you corrected it.

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Answer 1

A graph of the given piecewise function is shown on the cartesian coordinate in the image below.

Domain = x.

Range = y.

In Mathematics and Geometry, a piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the given piecewise-defined function, we have the following domains;

Domain = x ≤ -5, for f(x) = -x - 7.

Domain = -5 ≤ x < -2, for f(x) = -3.

Domain = x ≥ -2, for f(x) = -|x - 1| + 4.

Therefore, the overall domain is given by;

Domain = (-∞, ∞), x, or all real numbers.

A range is the set of all real numbers that connects with the elements of a domain;

Range = (-∞, ∞), y, or all real numbers.

Complete Question:

`f(x)=\left\{\begin{array}{Ir}-x-7, & \text{if } x < -5\\-3 ,& \text{if } -5 \leq x < -2\\-|x-1|+4, & \text{if } x \geq -2\end{array}\right`

Graph the given piecewise function.

Find the domain and range.