MHF4U - Unit 3 - Rational Functions

Lesson 1 - Reciprocal of a Linear Equation

• Rational Function - The quotient of polynomials in which the denominator has a degree of at least 1

  • The general form of a reciprocal of a linear function is f(x) = 1/(kx-c)

• The parent function is f(x) = 1/x

  • It has asymptotes at x = 0 and y = 0

  • It is always decreasing

• When x = c/k, y is undefined

• Vertical Asymptote - A line that the graph of the function approaches and never touches

• Horizontal Asymptote - A line that the graph of the function approaches as x approaches ∞ and -∞, but can be crossed in between

• At different intervals, the following can be considered:

  • Sign of the function

    • If the function is above the x-axis, it is +

    • If the function is below the x-axis, it is -

  • Sign of the slope

    • If the slope is increasing, it is +

    • If the slope is decreasing, it is -

  • Change in the slope

    • If the slope becomes more positive, it is +

    • If the slope becomes more negative, it is -