Here is an example to understand these steps. Example: Graph the piecewise defined function f (x) = ⎧ ⎨⎩−2x, x <−2 −|x|, −2 ≤ x ≤ 0 2−x2, x> 0 f (x) = {− 2 x, x <− 2 − | x |, − 2 ≤ x ≤ 0 2 − x 2, x> 0. Solution: f (x) has 3 definitions: -2 x when x is less than -2 and this is an exponential function.

You learned how to apply this knowledge to graphing piecewise functions—which are made up of other functions that are on restricted domains—which requires you to graph each piece on their respective restricted domains of the function.

Mar 13, 2025 · We can use our limit taking skills for the individual pieces in order to graph a piecewise function. Sketch f(x) = ⎧⎩⎨⎪⎪1 −x2 3 2x x> 1 x = 1 x <1 f (x) = {1 − x 2 x> 1 3 x = 1 2 x x <1. We start by graphing the individual functions inside of our piecewise. Then plot the parts of them that are used together on on graph:

How To: Given a piecewise function, sketch a graph Indicate on the x -axis the boundaries defined by the intervals on each piece of the domain. For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.

Given a piecewise function, sketch a graph. Indicate on the [latex]x[/latex]-axis the boundaries defined by the intervals on each piece of the domain. For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.

To write a piecewise function from a graph, first write functions for each interval on the graph. Secondly, combine them into one function with the rules for each interval. Substitute the value of x into the function rule for the interval where x falls to solve a function for f(x) or y.

To graph a piecewise function, it is a good idea to follow these steps. Look at the inequalities rst. Draw a dotted vertical line for each of these values. Marking lightly, graph all the functions which are given for f. Looking back at the inequalities, darken in the functions between the vertical lines for which they are valid. Example 2.

Example 1: Sketch the graph of the piecewise-defined function . (𝑥)= {2𝑥+3 if 𝑥 Q−2 −𝑥2 if −2<𝑥 Q2 √𝑥−2 if 𝑥>2 (Once again, keep in mind that the point (0,4)is not part of the graph because the input 0 is not part of the domain of the first piece. Now I will make …

4 days ago · Given a piecewise function, sketch a graph. Indicate on the \( x \)-axis the boundaries defined by the intervals on each piece of the domain. For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.

The following video walks you through the process of graphing a piecewise function. summary In this lesson, you learned that in cases where you want to sketch only a part of a graph, you would graph a function on a restricted domain , which is part of (but not the entire) domain of a function.