Graph each function. See Examples 1 and 2.h(x) = √4x

Question

Accepted Answer

Welcome back. I am so glad you're here. We are asked to plot the given function. Our given function is G of X equals the square root of 11 X. Then we are given a blank graph. We have a vertical Y axis, a horizontal X axis. They come together at the origin. The range for what's drawn for our Y axis is from negative five to positive 20. And the domain for what's drawn for our X axis is al is from negative five to positive 25. All right. So we take a look at our given function and we want to figure out what its base function is or in other words, what's happening to the X? And here we're taking the square root of X. So that base function is Y equals the square root of X. We recall from previous lessons that the graph of Y equals the square root of X is going to begin at the origin. And then it's going to go out into the first quadrant. It's going to head toward positive infinity for both X and Y values, but heading toward positive infinity for X faster than it's heading toward positive infinity for Y. Now this is just approximate, it is not an exact graph. Now, what we want to do is look at our given function and see what's different, what's different from the base function. And the difference is ours is being multiplied by this 11. Before we take the square rut of that X. So when we are multiplying a number directly to our X, before we take that square R, that's going to indicate a horizontal change. And because that number is larger than one, it's indicating horizontal shrinking. So essentially, we're gonna start at the origin still, but we're gonna shrink it horizontally. So it's gonna come up a little bit faster. Now, that's just an approximation of what it looks like. We can be more specific by creating an XY table, choosing a few values for X plugging those into our function square of 11 X, finding the corresponding Y values and plotting those points that we do understand generally what is happening with our function. And it gives us a good clue as to what X values to pick, we can see the domain of our function is from zero to positive infinity. So for our X values, I'm going to choose 01 and 11. Now let's plug those in and see what we get. So for zero, we're taking the square root of 11 multiplied by zero. Well, 11 multiplied by zero is zero and the square root of zero is zero. So yes, we're still at the origin there and we still have that point at 00. Now, let's try for one. So we have the square rut of 11 multiplied by one and 11 multiplied by one is 11. So we have the square root of 11. Now, with the square root of 11, that's going to be somewhere between three and four. So plotting this point for the X value of one, we go to the right one and for the Y value of the square root of 11, we're going up between three and four. So a little bit higher than what I drew. Now, an X value of 11. So we're taking the square root of 11 multiplied by 1111, multiplied by 11 is 121 and the square root of 121 is 11. So our last point is 1111 from the origin, we go to the right 11 and then we go up 11, which I think is right where I drew it. So that's pretty darn close. Now, what we can do is connect those points as smoothly as possible. And there we have our G of X equals the square root of 11 X. Well done. We'll catch you on the next one.

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Graph each function. See Examples 1 and 2.h(x) = √4x

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