Answer the questions about the following function. Is the point negative sqrt 10, one on the graph. So remember this is our input or our domain and this is our output. So we're going to put F of X being one because it's the output 20 times negative root 10 ^2 over negative root 10 to the 4th plus 100. We're going to see if this is a true statement or not. Well, negative root 10 times negative root 10 is 1010 * 20 is 200. So this numerator simplifies to 200 down here. Negative root 10 to the 4th negative root 10 times negative root 10 is 10, then times two more of those. So 10 * 10 is a hundred. 100 + 100 is 200. 200 / 200 is indeed one. So yes, it's on the point. The next part says what happens when X is 2. So we really want to find F of two. We're going to stick 2IN every time we see the X 20 * 2 ^2 / 2 to the 4th plus 100. That's going to give us 2020 ninths. When we simplify it, 20 * 2 ^2 2 ^2 4 four times 20 is 80. 2 to the 4th is 16116, and that reduces to 2020 ninths because they're both divisible by 4. So the next part says use this information to list it as a point, and they want you to really practice that. When the input is 2, the output is 2020 ninths. So when the domain was 2, the range was 2020 ninths. Part C says if F of X equal 1, what is X? So now we're going to say 1 equal twenty X ^2 / X to the 4th plus 100. We're going to cross multiply to get rid of our fractions. So X to the 4th plus 100 equal 20 X squared. We need to get everything to one side, X to the 4th minus twenty X ^2 + 100 = 0. We're going to factor this X ^2 * X ^2 gives me X to the 4th and the two numbers that are going to multiply to give me 100 but add to give me -20 is going to be -10 and -10. So this tells me that X ^2 = 10 twice. So X is positive or negative sqrt 10. So when F of X equal 1, IE the output is one, the range is one, the domain is negative root 10 and root 10 and follow the directions. It tells me I have to type it exactly and I have to use a comma to separate the answers. The square root button is over here, so pay attention to that. Back here in the last one it said we had to type it as an integer or fraction. That was simplified, so that's why we use 2020 ninths. Looking at the other parts, it said it asked us to put it as a point. So X negative root 10, Y1 root, 10, one. So Part D says what's the domain? And we want to remember that the domain just means what values can we use? Well, the denominator can never ever ever equal 0. Well, if we have X to the 4th plus 100X to the 4th is always going to be a positive number or zero. So 0 + 100 is never ever going to give us zero out or a positive plus 100 is never going to give us zero out. So the domain is going to be all real numbers. Negative Infinity to Infinity over here is my Infinity sign. In this palette list, the X intercepts. The X intercepts mean that the Y is 0. So if the Y is 0, we're going to have zero equaling twenty X ^2 X to the 4th plus 100. When I cross multiply the X to the 4th plus 100 * 0 gives me 0 equaling 20X squared. Solving for XI can see it's going to equal 0. the Y intercepts to get the Y intercept, it tells me that the X is 0. So for over here for the Y intercept we're going to say F of 0 or our y = 20 * 0 ^2 / 0 to the 4th plus 100. Well, 0 / 100 simplifies to 0, so our Y is 0. I think that was the last piece to that one, yes.