In Exercises 107-118, begin by graphing the cube root function, f...

Question

In Exercises 107-118, begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. -∛(x+2)

Accepted Answer

Hello, today we're going to be graphic G of X as a transformation of F of X. So for F of X, we are given F of X is equal to the cube root of X. And for G of X, we are given the negative cube root of the quantity X minus four. So before we graph G of X, let's get an idea of what the shape of F of X is going to be. While F of X represents the traditional cubic graph as the cube root of X is going to have its starting point at the origin zero comma zero. And the graph of this is going to have a snake like shape to it. So this is going to be the graph of F of X. Now let's go ahead and identify what transformations we're going to need to go from the function of F of X two G of X. While here we're going to have to transformations in total. The first transformation is going to evolve the quantity X minus four because this quantity is closely related to X minus H which indicates that there's going to be a horizontal shift in the quantity X minus 44 takes the spot of H. So H is going to equal to four, which means we have a horizontal shift of four units to the right. So that's gonna be our first transformation. The second transformation is going to be the negative sign in front of the function of G of X because the negative sign flips the graph along the X axis. So let's go ahead and apply our first transformation to the current form of F of X. So if we draw another graph, What we are first doing is shifting this entire graph for units to the right. So the new starting point of G of X is going to be at the .40 and the shape of the graph is going to stay unchanged for this transformation. So this is going to be the shape of the graph with the first transformation. Now let's go ahead and apply our second transformation. So again, the graph is still going to have its starting point at 4:00. But the negative sign is going to flip the graph with respect to the X axis. So the shape of the graph is now going to look like this and this is going to be the graph of G of X as a transformation of F of X. So let's go ahead and see which option accurately represents this. Now The option that accurately represents this graph is going to be be because it's starting point is at 4:00 and the shape of the graph is flipped with respect to f of X. So that means that B is going to be the answer to this problem. So I hope this video helps you in understanding how to graph using transformations. And I'll go ahead and see you all in the next video.

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In Exercises 107-118, begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. -∛(x+2)