Let

Question

Let $f\left(x\right)=\frac{x^2-4}{x-2}$ .

Calculate $f\left(x\right)$ for each value of $x$ in the following table.

Accepted Answer

Welcome back everyone. In this problem, we want to evaluate F of X equals X squared minus 25 divided by X minus five. For all values of X in the table. Here, we have our table with our missing values ranging from 4.9 sorry, ranging from X equals 4.9 to X equals 5.0001. And for our answer choices, we have the possible values ranging in ABC and D, OK. So in order for us to solve, we will need to figure out what the possible values are and substitute them into our table. And then we will compare them to our answer choices. Now to figure out the values of F of X, what we're really going to do is just substitute our values of X into our function to solve. So let's go ahead and start to do that. Let's start with our first value for X equals 4.9. Now at X equals 4.9 then our function we can call it F of 4.9 is going to be equal to 4.9 squared minus 25 divided by 4.9 minus five, which is going to be equal to 9.9. So we can write 9.9 where X equals 4.9. Now let's move on to the next part of our problem. OK. At F sorry, at X equals 4.99. No, we're going to substitute 4.99 into our function. And F of 4.99 equals 4.99 squared minus 25 divided by 4.99 minus five, which equals 9.99. So that means when X is 4.99 F FX is 9.99. Now, at this point for one, I think you probably see what we're doing here. We're just taking the values of X and plugging it into our function to solve. So I don't think I need to write or rest in order to save time. But also you may see a pattern here when it was 4.99. F FX was 9.9. When X was 4.99 F FX was 9.99. So that means at X equals 4.999 we can tell that F FX will be 9.999 and when X is 4.9999 then F FX will be 9.9999. Now notice here that we've skipped five and we're at 5.1. We can tell though that the same pattern will likely follow. OK. So let's substitute and try to figure it out at X equals 5.1. Now at X equals 5.1 F of 5.1 is going to be equal to 5.1 squared minus 25 divided by 5.1 minus five, which equals 10.1. So when X is 5.1 F FX is 10.1 next add X equals 5.01 then F of 5.01 is going to work out to be 10.01. So we can put 10.01 in our table. And again, based on the pattern, this tells us that when X equals 5.001 F FX equals 10.001. And when FF sorry, when X equals 5.0001 F of X equals 10.0001 this is our completed table of F of X for all the values that we wanted to figure out. Now when we go ahead and compare our table to all of the values in our answers, we can tell that D table D has the correct answers. Thanks for watching everyone. I hope this video helped.

Let $f\left(x\right)=\frac{x^2-4}{x-2}$ . <IMAGE>
Calculate $f\left(x\right)$ for each value of $x$ in the following table.

Key Concepts

Rational Functions

Simplifying Rational Expressions

Evaluating Functions

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