Question

Explain how to find zeros of rational functions.

Answer 1

Rational functions are functions which can be written as a ratio of two polynomials. We might recall that a polynomial is an algebraic expression in which the exponents of all variables are whole numbers and no variables appear in the denominator.

ZEROS: When discussing polynomial functions we were often interested in the zeros of the function. That is, we want to know the values in the Domain (input) of the function that would make the Range (output) equal to zero. At this point, graphs of functions typically show the domain on the horizontal axis - this means that the zeros would show up as the values on the horizontal axis where the graph touches or crosses.

When a rational function is equal to zero (that is, its output is equal to zero) then its Numerator is equal to zero. So, to find the zeros of a rational function we simply find the zeros of the Numerator .

Example : Let     The zeros of the function h(x) described above would be found by setting the Numerator equal to zero.
That is, 3x - 6 = 0
The zero is x = 2

Y-INTERCEPTS: The point where the graph crosses the y axis is called the y-intercepts. At that point the x-coordinate will always be 0. So, to find the y-intercept you just replace x with 0.

Example : The y-intercept of the function h(x) described above is h(0) = -6/5.