Google Клас
GeoGebraGeoGebra Клас

Rational Functions and Restricted Domain

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______________