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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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