Roots and powers Sketch a graph of the gi...

Question

Roots and powers Sketch a graph of the given pairs of functions. Be sure to draw the graphs accurately relative to each other.

y = (x)¹⸍³ and y = (x)¹⸍⁵

Accepted Answer

Welcome back, everyone. For the following functions, draw your graphs in the same Cartesian plane and label them accordingly. F X equals X 17th and the G of X equals X 19th. Here we have a graph that we can use to draw F of X and G of X. Now if we're going to draw the graphs of FF X and G of X, then we'll need a table to know their values, OK? So let's set up a table with X, FF X, and G of X, OK? And now for our table. If we were to choose some values of X, notice that on our graph, it increases by 0.5 in on the X and Y axis, OK? So if we start X at -2 and go to -1, 0.5, 0, 0.51, and then stop at 2, then we'll have a few points that we can use to plot our graph, OK? So now let's do that. OK. So we need to find the values of FF X and the G of X or these given values of X. Now we're going to do one together, OK? And then I'll allow you to do the rest in the interest of time, OK? But let me just fix this table a little bit. Uh, I, I'll allow you, like I said, to do the rest in the interest of time, but let's just do one or two to see how we would get those points. So when X equals -2, for example, Then F of X. Or if of negative 2 rather. would be equal to -2 raised to the power of 1/7, OK? And that is going to be equal to -1.104. On the other hand, G of -2. Would be equal to -2 to 19th, and that would be equal to -1.08. So now, on our graph, let's put F of X to be -1.104 to 3 significant figures and X equals 2, sorry, 4 significant figures, X equals -2, and -1.08, OK, 4 G of X. As I said, I'll allow you to do the rest, but you can compare your answers to mine. Uh, when X equals -1, then both F of X and G of X should be -1. When X is -0.75, F of X is -0.906, while G of X is -0.926. When X is 0, both FF X and GFX are 0. When it's 0.5, FF X is 0.906, while GFX is 0.926. When it's 1, both FFX and GFX are 1, and when it's 2, FFX is 1.104, and GFX is 1.08. Now that we have values of FOX and GFX from X going to negative 2 to 2, then we can plot our graph. So let's plot FFX in red and then I'll plot GEX in blue, OK? Now, starting with F of X, we go to our graph, when X is -2, F of X is -1.104, so it probably would be somewhere here as an estimate. OK. When it's -1, FFX is -1, when it's 0.5, FFX is -0.906. When it's 0, FFX is 0, 0.5, 0.906, 11, and 2, 1.104. Now we can go ahead and connect our graph. Try to draw as smooth as a curve as possible through our graph to show the graph of F of X. Next, let's do it for a GFX. When X is -2, GFX is -1.08. When it's -1, GFX is -1. -0.5, 0.92600. 1, sorry, 0.5, 0.926. OK. Uh, 101. I think I should be a little bit above it. That's one. 11, OK, and 2 1.08, probably somewhere here. Now, we can go ahead and draw our curve to the best that we can. And now in blue, that will be G of X. Thus, this graph represents the graph of FF X and GFX respectively. Thanks a lot for watching everyone. I hope this video helped.

Roots and powers Sketch a graph of the given pairs of functions. Be sure to draw the graphs accurately relative to each other.

y = (x)¹⸍³ and y = (x)¹⸍⁵

Key Concepts

Roots and Powers

Graphing Functions

Behavior of Radical Functions

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