Graph each function. See Examples 1 and 2. ƒ(x)=2/3|x|

Question

Accepted Answer

Hello, everybody doing. All right. Today, today we're going to bring on this question that states for the following function sketch its graph where the function is F of X is equal to 1/7 multiplying the absolute value of X. Now for a question like this, the first thing I want to ask myself is what would the parent function be here? And is there a parent function here? In our case there is, there is. So the parent function would be F of X is equal to the absolute value of X. So what does this mean? This means that our graph will have the same general shape. In this case, the 1/7 in front is multiplying our values of X and multiply by 1/7 is the same as dividing by 1/7 or dividing by seven. So the values of X would be shrunk by seven units because we're dividing each value by seven. So our graph would be shrunk. The graph of the absolute value of X would be shrunk by seven units in our function here. And finally, because all we're doing is shrinking, we're not moving um the Y values the Y values aren't changing, we'll still have a vertex at zero, comma zero. So the origin will still be your vertex. So now I'm gonna try two different points just to have an idea. We, we have the vertex of our graph. It's going to look like the absolute value graph which an absolute value graph usually looks like a V. It's in the shape of a V above the X axis because since we're absolute value, we only obtain positive values of Y. So we're on always above the X axis. So we'll have a V coming out of the origin and extending left and right. So now let's say X equals negative 21. That's the point I'll be trying. That means we'll have F F of negative 21 which will be equal to 1/7 multiplying the absolute value of negative 21 and that is equal to 1/7 multiplying positive 21 because the absolute value of negative 21 is positive 21. And this is the same as dividing 21 by seven. So we'll have that F of negative 21 is equal to three or the points negative 21 comma three. Now let's try a different point. We'll try X is equal to positive 21. So I have that F of 21 is equal to 1/7 multiplying the absolute value of 21. And this is the same as same 1/7 multiplied by 21. And once again, this is the same as saying 21 divided by seven, which is three. So we'll have that f of 21 is equal to three or the 0.21 comma three. So now we have three points. So we'll have negative 21 comma three, the vertex at zero, comma zero another point at 21 comma three. So with this information, we can go ahead and make an a, uh a general graph of what our function is. So we draw a Y axis and an X axis and I'll have the X axis go upwards in terms of seven. So I'll draw a line at seven a line at 14 in a line at 21. And the same for the negative axis, we have a line at negative seven a dash at negative 14 and another one at negative 21 as for the Y value I'll go in terms of three. So my first line will be three, my second line will be six. My third line will be nine, fourth line will be 12. So now I can plug in the points that I have, which is one point at the origin, one points at 21 comma three and another point at negative 21 comma three. So now I can connect those dots and the graph will extend past those points, continue to extend, extend past those points and we can live all our points. So negative 21 comma three zero, comma zero and 21 comma three. And as you can see, the graph looks like exactly what we talked about. It's a V above the X axis. So always positive, but it's very, it's stretched out because or it's shrunk, the values of why are shrunk. Therefore, the graph is wider. So I hope that was helpful. And until next time.

Graph each function. See Examples 1 and 2. ƒ(x)=2/3|x|

Key Concepts

Absolute Value Function

Vertical Scaling

Graphing Techniques

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