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? What is its domain?

Accepted Answer

Hey, everyone here we are asked to determine which of the following is the graph of F of X is equal to the square root of eight X. And we are also asked to find its domain here we have four answer choice options. Each of which display a graph of our given function and state some domain answer choice A states we have a domain from negative infinity to zero. Included answer choice B states we have a domain from zero, included to positive infinity answer choice C states we have a domain from negative infinity to positive infinity. And finally answer choice D states we have a domain from negative infinity to positive infinity. So now to begin solving this problem, we first want to focus on graphing our function. So as we recall, the given function is F of X is equal to the square root of A X. So to graph this function, we just need to consider arbitrary values of X. And so we also need to notice that we have the square root of A X, which means that our arbitrary value of X must be greater than or equal to zero. Since we do not want to take the square root of a negative term. So again, we need to have A X be greater than, or equal to zero or that X must be greater than or equal to zero. So now with this in mind, we can first consider the value for when X is equal to zero. So we just need to set 04 X in our function to find our output. So we have F of zero is equal to the square root of eight times zero. In simplifying we just get zero. So this shows us that one of our ordered pairs is going to be zero and zero. So now we want to repeat this process again using values that are greater than or equal to zero. So we can create a table of values of which we can plot them on a graph. So we can choose any values for X. But let, let's choose 0123 and four. And now we substitute each of these values in two hour function to get our Y values. So we get 2.834, 4.9 and finally 5.66. So now here we see we have five different ordered pairs. So the next step is to plot each of these points on a graph. And so now we see we have four or sorry, five different points of which we can graph. And so with these plotted points we now want to draw a smooth curved line which passes through all of these points. And so in doing so we get the graph of our function F of X. So with this smooth curved line drawn for our function, we can now determine the domain of this function. So to determine the domain, we just need to assess our graph and we need to look at our X values and we see we go from zero and then we go all the way to a positive infinity. Now infinity is always excluded. So it gets closed by a parentheses and zero. In this case, we know is included since one of our points is at the origin. So zero gets closed by a bracket. So now with our graph drawn of our function F of X, as well as our domain identified, we see here that we are left with answer choice B 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? What is its domain?

Key Concepts

Square Root Function

Domain of a Function

Graphing Functions

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