Answer the questions about the following function. f(x) =...

Answer the questions about the following function. f(x) = \frac{x+8}{x-11} (a) Is the point \left(4, -\frac{15}{4}\right) on the graph of f? (b) If x = 1, what is f(x)? What point is on the graph of f? (c) If f(x) = 2, what is x? What point(s) is (are) on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f.

Transcript

00:01 This problem gives us f of x equal to negative 3 x squared plus 5 x and asks us a bunch of questions about this function.

00:06 First is if negative 1 2 is on the graph.

00:09 To be able to determine that, we'll evaluate at f of negative 1 and see if the result is 2.

00:16 So negative 3 times negative 1 squared plus 5 times negative 1.

00:20 Negative 1 squared is 1 times negative 3, but state negative 3.

00:24 5 times negative 1 is negative 5.

00:26 Negative 3 minus 5 is negative 8.

00:28 And it was supposed to be 2.

00:30 So the answer to that is no, it's not on the graph.

00:33 The next two give us either an x or a y want us to find the corresponding value that goes with it.

00:39 So first one, if x is negative 2, what is f of x? so we'll evaluate at negative 2 and see what f of x comes out to.

00:47 So negative 3 now times negative 2 squared plus 5 times negative 2.

00:53 So that will give us negative 2 squared, which is 4 times negative 3 is negative 12.

00:57 5 times negative 2 is negative 10.

01:00 Negative 12 minus 10 is negative 22.

01:02 So when x is negative 2, f of x is negative 22.

01:06 And as a point, that would be negative 2, negative 22 as an x -y point.

01:14 The next one kind of goes in reverse and gives us the y value, the f of x value, and wants to know the x value or x values that goes with it and what their points would be.

01:22 So we'll set negative 3x squared plus 5x equal to negative 2.

01:28 See what we can do to solve.

01:29 And i'm going to try to factor, so i'll add two over.

01:35 And then i'm going to factor out the negative leading coefficient, just so we can keep that to the side and just focus on this positive leading coefficient of 3x squared.

01:44 And to be able to factor this trinomial, we'll have to do a times c, which is negative 6...

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