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Graphing Functions by Making a Table - Example 1

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

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Video Transcript

All right. So in this example, we're being asked to graft the function F of X is equal to negative two X plus three by making a table of values. So, as you can see, I set up a table of values here in our second column, we're gonna put in our function expression, which is negative two X plus three. So remember to graph of function by using a table of values, you can substitute in any values effects that you want to find the corresponding why values. So I'm going to start by substituting in negative one for wraps. So that means I need to find f of negative one. So they do this, we're gonna substitute negative one in place of X, so have negative two times negative. One plus three. Well, negative. Two times negative. One is positive. Two and two plus three is five. So f of X is five, which means it's corresponding. Ordered pair will be the ordered pair. Negative 15 That means this point falls on a graph. So let's plot it so we'll go left one and up. Five. All right, let's plug in a different value for X. How about zero. So we need to find f of zero. So again, we're going to substitute zero in place of X. So we're gonna have negative two times zero plus three. Well, negative. Two times zero is zero. So this term essentially cancels out, so we're just left with positive three. That means the ordered pair 03 falls on our graph. So let's plot it. So x zero. So we won't move off the right, so we just simply need to go up three. Alright, let's try. Never value. How about one? We're gonna find f of one, so we'll substitute one in place of exile. What? Negative. Two times one plus three. Well, we have negative two times one or Sorry. Yep. Negative. Two times negative One. Which is positive to Sorry. I realized I substituted negative one in instead of positive one. I knew something looked a little weird there. Let's try this again. We're substituting positive one in place of ax. There we go. All right. Well, negative. Two times. One is negative. Two and negative. Two plus three is positive one. So that tells us the ordered pair 11 falls on our graph. So we'll go right one and up. One. Well, have you noticed a pattern? Because a lot of times you'll see patterns with functions every time we increase one for X r ffx values decreased by two. So, just out of curiosity without actually substituting to in place of X, what should this corresponding f of X value be? It should be negative one. And again, you could check by substituting to into your function and just to prove it for you. Negative two times two is negative. Four and negative four plus three is negative one. So once you find the pattern, that can also help you to. So that means the ordered pair to negative one falls on our line, so we'll go right to and down one. So, as you can see as we increase by one for our X values are why values go down by two. So we could actually kind of extend this graph to see that it looks like a line, and in fact it should be a line. So now that we have all these different points, what we can do is graft the line that goes through them. And if you have a ruler that will help you, which I definitely don't want using the computer. Perfect. Now here we have graft. The function f of X equals negative two X plus three on what we find is its graph is a line.