College Algebra 9th txtbk

SECTION 4–4 Rational Functions and Inequalities 301
Z Figure 3 (continued)
y
y
y
15
3
2
5
5
x
3
3
x
10
10
x
15
3
2
(d) F (x) x2 3x
x 1
(e) G(x) x 1
x 3 4x
(f) H(x) x2 x 1
x 2 1
EXAMPLE 2 Properties of Graphs of Rational Functions
Use Theorem 1 to explain why each graph is not the graph of a rational function.
(A) y
(B) y
(C)
y
3
3
3
3
3
x
3
3
x
3
3
x
3
3
3
SOLUTIONS
(A) The graph has a sharp corner when x 0, so Property 2 is not satisfied.
(B) The graph has an infinite number of turning points, so Property 4 is not satisfied.
(C) The graph has an infinite number of zeros (all values of x between 0 and 1, inclusive,
are zeros), so Property 3 is not satisfied.
MATCHED PROBLEM 2
Use Theorem 1 to explain why each graph is not the graph of a rational function.
(A) y
(B) y
(C)
y
3
3
3
3
3
x
3
3
x
3
3
x
3
3
3