Graph each function. See Examples 1 and 2. ƒ(x)=-√-x

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Welcome back. I am so glad you're here. We're told for the following function sketch its graph. Our function is G of X which equals negative square root of and then inside the radical is negative 25 X. All right, we can begin to sketch this graph with a very rough sketch of a coordinate plane. We have a vertical Y axis, horizontal X axis, they come together at the origin in the middle. Now we have two paths we can go down here, we can identify the base function and all of its transformations. And the other path is we can create an X Y table and plot some points. So I'll demonstrate both of those for the base function. The base function here is so this is our F of X and is taking the square root of X. And we recall from previous lessons that the square root of X as a function graph starts at the origin and then it's going to occupy only the first quadrant. It's going to head toward the positive values for X for infinity much quicker than it's heading toward the positive values for Y. So it will curve more quickly toward positive infinity for X than it does for Y. So there's our F of X. Now, what are the transformations taking place? Well, we have this X being multiplied by a negative 25. The fact that it's being multiplied by a negative indicates that there is going to be reflection because that's being multiplied directly to the X inside of that radical. It's reflection over the Y axis. Now it's being multiplied by negative that 25 being multiplied by the X because that's being multiplied directly to the X inside of the radical, that indicates horizontal because that number is greater than one, that 25 specifically is greater than one. It's horizontal shrinking by a factor of 25. Now, the only other transformation here is this negative being multiplied on the outside of the rad radical that's happening not directly to the X. So that indicates reflection over the X axis. So from this, if we want a very imprecise graph, we know that we're going to flip it over both the X and the Y axis, that means it's going to be entirely in the third quadrant and then there's some horizontal shrinking. So from the origin, it's going to head toward negative infinity for X and Y and still heading toward negative infinity for the X values more quickly than the Y values. So it'll look something like that. Now, to be very precise, we can create an X Y table and plot a few points. We know that when we put zero in for X, we'll get zero for Y. So that's one of our points at the origin. We know that now we could choose a value, we know that our domain and range here is just going to be from zero to negative infinity for both X and Y. So for our X values that we choose, we just want to choose negative X values, we could choose a negative four and plugging that in for X, we are going to get a negative 10 for Y value. So we could claim that one of these points here is negative for a negative 10 or we could plot it more precisely. I'll plot, plot it more precisely. So from the origin, going to the left four units for the X value of negative four and then going down 10 units for a Y value of negative 10. So I didn't draw my horizontal shrinking very well. Now, if we plug in for an X value negative 25 we're going to get a corresponding Y value of negative 25. So plotting that point from the origin, we go to the left 25 units and we go down 25 units. So that will look something like this. We can draw, connect these heading toward negative infinity for our X and Y values. And there's our graph well done. We'll catch you on the next one.

Graph each function. See Examples 1 and 2. ƒ(x)=-√-x

Key Concepts

Graphing Functions

Domain and Range

Transformations of Functions

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