 # 3.7 Graphs of Rational Functions

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3.7 Graphs of Rational Functions
Definition: A rational function is a ratio of two polynomials, providing that the polynomial in the denominator is not the zero polynomial. Examples: An example that is not a rational function is

Finding the domain of a rational function
The domain of a polynomial function is the set of all real numbers {x|(-∞ <x<∞)}. The domain of a rational function is restricted to real numbers that do not cause the denominator to equal zero.

Example 1: Find the domain of
Set the denominator equal to zero and solve for x The domain is (-∞, -7)U(-7, ∞)

Example 2: Find the domain of
Set the denominator equal to zero and solve for x X=0 The domain is

Example 3 Find the domain of f(x)=
Set the denominator equal to zero and solve for x. Factor: (x+3)(x+2)=0 Set each factor equal to zero and solve for x The domain is (-∞,-3)U(-3,-2)U(-2,∞)

Example 4 Find the domain of f(x)=
Set the denominator equal to zero and solve for x. Factor: (x-2)(x+1). Observe that (x-2) is a factor in the numerator. Do not re-write the equation as f(x)= Set each factor equal to zero and solve for x x-2=0, x=2 x+1=0, x=-1 The domain is (-∞,-1)U(-1, 2)U(2,∞)

Example 5 Find the domain of
Set the denominator equal to zero and solve for x does not factor