Question 1
A) What is a rational function?
A rational function is a function where both the denominator and the numerator are polynomials.
The polynomial in the rational function denominator cannot be zero.
B) How is it different from a polynomial?
All rational functions have two polynomial functions in it. However, not all polynomial functions
are rational functions. A rational function is a ratio of two polynomials functions.
Examples of polynomial functions could be f(x)=
7x
3
+x
2
-2 and g(x)= x+5. An example of
rational functions can be h(x)= f(x)/g(x).
Another difference between polynomials and rational functions is that rational functions have
both vertical and horizontal asymptotes.
C) Provide a graph of each to demonstrate the difference.
A rational function:
A polynomial function:
F(x)= (x
2
+5) / (x-3)
h(x)= 2x
2
+4x-2

Question 2
For the following functions, find:
X-intercept
Y-intercept
holes
Vertical asymptote
A) f(x)= (2x
2
-5) /
(x
2
)
Light blue answers are x-
intercepts.