GeoGebra Worksheet 3: Rational Functions and Restricted Domain
Part I
Lesson Objective: Building on knowledge of domain, range, slope, and intercepts, write a linear function defined by a set of given parameters. Experiment with GeoGebra tools to check answers.
Lab Overview: This lab features several different rational functions, each color coded to match a slider value. Adjusting the sliders will alter the equation of the function, thereby changing its domain restriction and resulting graph. Vertical asymptotes are also displayed for certain functions.
Directions: Determine the equation of a line which has the following properties. Write answers in Slope Intercept Form.
1. Slope = 2 y-Intercept = 1
_____________________________________
2. Slope = -3 Passes through (-3, 5)
_____________________________________
3. Passes through (1, 6) and (4, 4)
_____________________________________
4. x-Intercept = -7 y-Intercept = 8
_____________________________________
Part II
Lesson Objective: Recognize restrictions on domain of a function and state vertical asymptotes.
Directions: State the domain of each function and determine its vertical asymptote.
1. f(x) = 1/x
Domain________________________ Vertical Asymptote___________________
2. f(x) = x/(x+3)
Domain________________________ Vertical Asymptote___________________
3. f(x) = 1/√(6-x)
Domain________________________ Vertical Asymptote___________________
4. f(x) = x/(x-11)
Domain________________________ Vertical Asymptote___________________
Directions: Consider the function f(x) = (x+a)/(x-b)
1. What value of a will result in a y-intercept of 2? _________
2. What value of a will result in a y-intercept of -3? _________
3. What value of a will result in a y-intercept of 10? _________
4. What value of b will result in a vertical asymptote of x= 1? _________
5. What value of b will result in a vertical asymptote of x= 9? _________
6. What value of b will result in a vertical asymptote of x= -6? _________
7. For f(x) = (x+1)/(x-4) , state the domain, y-intercept, and vertical asymptote
Domain _________________ y-intercept _______________ vertical asymptote______________