Rational Expressions and Functions
11.1 Simplifying Rational Expressions
1) A rational expression is simply the quotient of two polynomials. See examples
presented in this section.
3)
a) The expression is undefined at  because
substitution of  into the
expression will yield a denominator of zero. Division by zero is undefined.
b) Y = (X – 3)/(X + 2)
c) When , Y1 the calculator reads ERROR.
5)
Table results:
b) The expressions are not equivalent at x = 2 because
substitution of 2 for x
in both expressions yield different output values.
For x = 2, ,which is
undefined. For x = 2, .
7)
9)
Skill and Review
19)
a)  is an exponential growth function. This
is because the
function is of the form  with b > 1 and k >
0. One could
conclude the graph of f is a growth function by observing that as x takes
on larger values, the value of the function f(x) increases.
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