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Sullivan Algebra and Trigonometry: Section 4.4 Rational Functions II: Analyzing Graphs. Objectives Analyze the Graph of a Rational Function. To analyze the graph of a rational function:. a.) Find the Domain of the rational function. b.) Locate the intercepts, if any, of the graph.

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sullivan algebra and trigonometry section 4 4 rational functions ii analyzing graphs
Sullivan Algebra and Trigonometry: Section 4.4Rational Functions II: Analyzing Graphs
  • Objectives
  • Analyze the Graph of a Rational Function
slide2

To analyze the graph of a rational function:

a.) Find the Domain of the rational function.

b.) Locate the intercepts, if any, of the graph.

c.) Test for Symmetry. If R(-x) = R(x), there is symmetry with respect to the y-axis.

d.) Write R in lowest terms and find the real zeros of the denominator, which are the vertical asymptotes.

e.) Locate the horizontal or oblique asymptotes.

f.) Determine where the graph is above the x-axis and where the graph is below the x-axis.

g.) Use all found information to graph the function.

slide4

b.) y-intercept when x = 0:

a.) x-intercept when x + 1 = 0: (– 1,0)

y– intercept: (0, 2/3)

c.) Test for Symmetry:

No symmetry

slide5

d.) Vertical asymptote: x = – 3

Since the function isn’t defined at x = 3, there is a hole at that point.

e.) Horizontal asymptote: y = 2

f.) Divide the domain using the zeros and the vertical asymptotes. The intervals to test are:

slide6

Test at x = – 4

Test at x = –2

Test at x = 1

R(– 4) = 6

R(–2) =–2

R(1) = 1

Above x-axis

Below x-axis

Above x-axis

Point: (– 4, 6)

Point: (-2, -2)

Point: (1, 1)

g.) Finally, graph the rational function R(x)

slide7

x = - 3

(3, 4/3) There is a HOLE at this Point.

(-4, 6)

(1, 1)

y = 2

(-2, -2)

(-1, 0)

(0, 2/3)