Graphing Rules

Rational functions

Have a horizontal AND Vertical asymptote

1. Find the Vertical asymptote

   • denominator= 0

   • graph can’t touch the asymptote

2. Find the Horizontal asymptote

   • compare the degrees of the numerator and denominator

     • denominator has a higher degree, horizontal asymptote is y=0

     • they have and equal degree, horizontal asymptote is the ratio of their leading coefficient

     • numerator has a higher degree, there is no horizontal asymptote

   • graph can touch and go through the asymptote

3. Find the x and y intercepts

4. Find Axis of symmetry

   • plug in f(-x) for f(x)

     • if it simplifies to the same thing, the axis of symmetry is the y-axis

     • if it simplifies to the opposite function or -f(x), the axis of symmetry is the origin

     • if it’s neither, there is no axis of symmetry

5. Plot points

   • pick x values and find their y values

Square root Functions

1. Use parent function f(x)= a√(x -h) +k to find the transformations

   • if a is negative, its a reflection over the x axis

   • if a is more than, it’s a vertical stretch

   • if a is between 0 and 1, it’s a vertical shrink

2. Create a table for the parent function y=√x to create a table of values

3. graph the parent function and then do the transformations

Logarithmic Functions

Have a vertical asymptote

1. Find the vertical asymptote

   • argument = 0

2. Create a table of values

   • Plug in x-values and find their y-values

3. Apply transformations

   • Apply the horizontal shifts of the function

Exponential Functions