Alright, let’s dive into the cool world of rational functions in algebra, particularly focusing on their domains and zeros. Think of a rational function as a fraction where both the numerator (the top part) and the denominator (the bottom part) are polynomials. It’s like having a fraction, but instead of plain old numbers, you have entire algebraic expressions sitting there!
Now, the domain of a rational function is basically all the possible values of x (the variable) that you can plug into the function without causing any mathematical mayhem. The biggest no-no in math? Dividing by zero. It creates a black hole in the math universe—totally undefined. So, when figuring out the domain of a rational function, your mission is to find out where the denominator equals zero and then exclude those x values.
On to the zeros of the function, which are sometimes called "roots." These zeros are the x values that make the whole function equal to zero. To find them, you just need to set the numerator equal to zero and solve for x.
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