To answer each question, refer to the following basic graphs. Whi...

Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x^3? What is its range?

Accepted Answer

Hey, everyone here we are asked to determine which of the following is the graph of F of X is equal to one half X cubed. And we also need to find its range here. We have four answer choice options. Each of which display a graph of F of X and each state sum range answer choices A and B have a range from negative infinity to positive infinity. And answer choices C and D stay a range from zero included to positive infinity. So to graph our given function, which again, as we recall is F of X is equal to one half X Q, all we need to do is consider arbitrary values of X. So we can begin by considering when X is equal to zero. Well, to find our output, we just have to substitute in 04 X. So we have F of zero is equal to one half times zero cubed. And now simplifying here, we just get zero when we have X is equal to zero. So we see that one of our ordered pairs in the graph is going to be 00. So now we want to repeat this process. And come up with a table of values for X and Y so that we can then graph our function. So we can choose different values for X. Let's say we have negative two, negative one, then we can include zero as well and then go to positive one and positive two. And now substituting individually each of these values for X, we get our Y values. So we have negative four, negative one half, zero, positive one half and positive four. And so now you see we have five different ordered pairs of which we now just want to plot onto a coordinate plane. So plotting, we see each of our individual points plotted on a graph. And so now the next step in graphing our function after plotting our points is to simply connect each of these points as a solid line. So connecting each of these points, we end up with our graph here again, which is a solid smooth line that passes through the points 241 and one half, 00, negative one and negative one half and finally negative two and negative four. So with this graph, we now want to determine our range. Again, this is the graph of our given function F of X. So now to determine the range, we just have to look at our Y values. And we see that we do not have any restrictions on our Y values. So our range for this function is simply from negative infinity to positive infinity and infinity is excluded. So both infinities get, get closed by parentheses. So now with our graph drawn and our range determined, we can now compare our solution with our answer choices and we see here that we match with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x^3? What is its range?

Key Concepts

Cubic Functions

Graphing Techniques

Range of a Function

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