Graph the following functions.

Question

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Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Sketch the graph of the following piecewise function. U of X is equal to curly bracket, -3 multiplied by X minus 2, if X is less than -2. For if -2 is less than or equal to X, and if X is less than or equal to 2. And X + 2 if X is greater than 2. Awesome. So it appears what we're trying to do for this particular problem is we're trying to ultimately sketch a graph of the of this particular piecewise function. So we're trying to graph this function of U of X. So, with that said, Let us first off split our three different since let's treat our piecewise function as 3 separate curves that we're plotting together as one, so let's break it up into 3 separate things that we're solving for. So first off, let us focus on the condition where, and let's write this in red, where X is less than negative to condition. So if X is if X is less than. -2, we need to note that for this particular case, where so when X is equal to -3, that will mean that U of X will be equal to 7, and when X is equal to -5, that will mean that U of X. Is going to be equal to 13. And this will mean, as we should recall and note that a line should pass through the points, or rather, specifically the coordinate points, -3.7, which, as we should recall, -3 denotes the X coordinate and 7 denotes the Y coordinate. So once again, this will mean that a line should pass through -3.7. And -5.13, and it should be on the left. So I'll say. L, so it's to the left of X equals -2. Awesome, and let's. Move this down to the bottom here, so we have a little bit more space. Awesome. So, moving right along here. So let's move on to our next condition. So our next condition that we need to consider that if X is from -2 to 2, so this is the condition from -2 to 2. And specifically 2 to 2. So if X is from -2 to 2, a line should pass through -2.4 and 2.4 and not be outside of these two points. And finally, for our last condition, if X is greater than 2, so when X is greater than 2, so when X is equal to 3, that will mean that you of X. In this case, so if, so this is when X equals 3, U of X will be equal to 5, and similarly, when X is equal to 4, that will mean that U of X will be equal to 6. And once again, like I, I didn't specify, but when we're saying that X equals -3, that's when we're plugging in the value for -3. In for X, so we're plugging in this value for x, and when we do, we will find that you of X will equal 7. So -3 multiplied by -3 will be 9 and 9 minus 2 gives us 7. So to specify to specify just in case we're confused. So with that said, Now, going back, so considering when X equals 3 and when X equals 4, we should know as a result that a line should pass through 3.5 and 4.6, and it should be to the right of, which I'll do a capital R, so to the right of X equals 2. So, with that said, using these pieces of information that we collected together based on these different conditions, when I plug in our different functions, which we need to consider, so you have X, so when you plug in these different these different expressions, so for these different conditions, and we plot our different curves, which in this case they're more like lines instead of curves since they're not. Like curved like a parabola, but still, we have these different lines for our three different conditions. So as we could see, we have a diagonal line going downwards. For our X is less than -2 condition, and then for when our X is from -2 to 2, we have our green line. Or our green curve. And then for our final condition, which is where X is greater than 2, we have our blue line, or blue curve going to the right. And that is it. That is how we sketch a graph of this particular piece-wise function. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Graph the following functions.
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error on line 1 at column 295: Unescaped '<' not allowed in attributes values
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Key Concepts

Function Graphing

Domain and Range

Transformations of Functions

Watch next

Graph the following functions.This page contains the following errors:error on line 1 at column 295: Unescaped '<' not allowed in attributes valuesBelow is a rendering of the page up to the first error.

This page contains the following errors:

Below is a rendering of the page up to the first error.

Key Concepts

Function Graphing

Domain and Range

Transformations of Functions

Watch next

Graph the following functions.
This page contains the following errors:
error on line 1 at column 295: Unescaped '<' not allowed in attributes values
Below is a rendering of the page up to the first error.