I do not understand how to complete rational functions: ie: As x (arrow) -3, f(x) (arrow) ?. Our book sucks and our instructor is little help. Thank you.

I'm sorry to hear that you're having trouble with rational functions! I'll do my best to help you understand how to complete them.

To find the value of a rational function as x approaches a certain value (in this case, -3), we can follow a few steps:

Step 1: Write the rational function as a fraction. A rational function is a fraction with polynomial expressions in both the numerator and denominator. For example, f(x) = (3x + 1) / (x - 2) is a rational function.

Step 2: Replace the variable x with the value it is approaching. In this case, we want to find f(x) as x approaches -3. So we substitute x with -3 in the rational function.

Step 3: Evaluate the expression with the substituted value. Simplify the numerator and denominator separately to find the resulting value. If the denominator becomes zero, the rational function is undefined.

Let's go through an example. Suppose we have the rational function f(x) = (2x + 5) / (x - 1), and we want to find f(x) as x approaches -3.

Step 1: The rational function is already in proper fraction form.

Step 2: Replace x with -3 in the rational function. f(x) = (2(-3) + 5) / (-3 - 1)

Step 3: Simplify the numerator and denominator. f(x) = (-6 + 5) / (-4) = -1 / -4 = 1/4

So, as x approaches -3, f(x) approaches 1/4.

I hope this explanation helps! If you have further questions or need additional examples, feel free to ask.