Precalculus

What are zeros in the context of a function?

Zeros are the x-values that make the function equal to 0 (numerator = 0, denominator ≠ 0).

What is the domain of a function?

The domain consists of all x-values that make the function valid (values that do not make the denominator = 0).

How do you find the y-intercept of a function?

The y-intercept is found by evaluating the function at x = 0.

What indicates the x-coordinate of a hole in a function?

The x-coordinate is the value that makes the canceled factor in the numerator and denominator equal to 0.

How do you find the y-coordinate of a hole?

Plug the x-coordinate of the hole into the simplified function after canceling the common factor.

What are vertical asymptotes?

Vertical asymptotes are x-values that make the denominator = 0 and do not cancel out (not holes).

What is end behavior in functions?

End behavior shows what happens as x approaches ∞ or -∞, determined by comparing the degrees of the numerator and denominator.

What happens if the top degree is less than the bottom degree in end behavior?

The horizontal asymptote is y = 0.

What happens if the top degree is equal to the bottom degree?

The horizontal asymptote is the ratio of the leading coefficients.

What happens if the top degree is greater than the bottom degree?

There is no horizontal asymptote, but there may be a slant asymptote.