Graph each piecewise-defined function.

Question

f (x) = {\begin{matrix} - 3 & if x \leq 1 \\ - 1 & if x > 1 \end{matrix}

Accepted Answer

Hey, everyone here we are asked to graph the following function F of X is equal to five. If X is less than or equal to two and two. If X is greater than two, here we have four answer choice options. ABC and D, each of which display a graph representing our given function. So the key to solving this problem is to grab each interval of the domain separately. So we can begin with the first interval of our function where we have F of X is equal to five if we have X is less than or equal to two. So we see that this function F of X is equal to five is just a horizontal line defined by Y is equal to five. So we see that it, it extends from negative infinity all the way to where, where X is equal to two according to our inequality. So with this information, we can graph this part of our function. So here we have the graph of Y is equal to five where we go from negative infinity all the way to where X is equal to two. So the end point of this part of our function is at the 20.0. and five. And at this point is a solid circle because we have that X is defined where XX is equal to two. So now that we have considered the first part of our function, we can move on to considering the second part of our function. So we have F of X is equal to two if X is greater than two. So its graph is again going to be a horizontal line since we have F of X is equal to two, which is defined as Y is equal, Equal to two. And we see that according to the inequality that the line will extend from two to positive infinity. However, we will have a hollow point as the end point since F of X is equal to two is not defined for X is equal to two. So now with all of this information, we can graph this second line. And so graphing, we see again, we have a line of Y is equal to two where we go from X is equal to two to positive infinity. And again, we have a hollow end point since X is not defined when X is equal to two. So now we have finished graphing both of our functions or both parts of our function. So our final graph results as two lines, the upper line has a solid endpoint and extends from negative infinity to X is equal to two. Then we go from XIS equal to two to positive infinity for our second lower line where the endpoint is a hollow circle. So with this finalized graph, we are left with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Graph each piecewise-defined function.
$f (x) = {\begin{matrix} - 3 & if x \leq 1 \\ - 1 & if x > 1 \end{matrix}$

Key Concepts

Piecewise-Defined Functions

Domain and Inequality Notation

Graphing Constant Functions

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