2 5 Rational Functions Rational Functions O Example

2. 5 – Rational Functions

Rational Functions O

Example 1: Find the domain and the equations of the vertical or horizontal asymptotes, if any. a. b.

Graphs of Rational Functions O

Graphs of Rational Functions O x-intercepts: Occur at real zeros of numerator. O y-intercepts: Value of the function when x = 0.

Example 2: For , determine any vertical and horizontal asymptotes and intercepts. Then graph the function and state its domain.

Example 3: For , determine any vertical and horizontal asymptotes and intercepts. Then graph the function and state its domain.

Holes: O Removable discontinuities. O When numerator & denominator have common factors. (Any factors that cancel. ) O Holes are at the zeros of the common factors. O Find the ordered pair at that x-value.

Holes:

Example 4: O Determine any vertical and horizontal asymptotes, holes, and intercepts for. Then graph the function and state its domain.

Example 5: Determine the vertical and horizontal asymptotes and holes of the graph of A. vertical asymptote at x = – 2, horizontal asymptote at y = – 2; no holes B. vertical asymptotes at x = – 5 and x = – 2; horizontal asymptote at y = 1; hole at (– 5, 3) C. vertical asymptotes at x = – 5 and x = – 2; horizontal asymptote at y = 1; hole at (– 5, 0) D. vertical asymptote at x = – 2; horizontal asymptote at y = 1; hole at (– 5, 3)

Solving Rational Equations O Find LCD & multiply each term in the equation by the LCD. O Check for extraneous solutions.

Example 6: Solve:

Example 7: Solve:

Example 8: Solve:

Example 9: Solve:

Example 10: Suppose the current I, in amps, in an electric circuit is given by the formula , where t is time in seconds. At what time is the current 2 amps?