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Name________________________________________ Period ______________________ H-Intro to Calc Study Guide for Lessons 1.1 and 1.2 Section 1.1: Modeling and Equation Solving 1. Analyze the following table about the average annual cost to care for a pet ocelot, and then answer the questions that follow: able 1.7 U.S. Air Travel Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Average Annual Cost $452.30 $475.10 $488.50 $528.80 $547.80 $581.20 $594.70 $612.90 $636.00 $666.10 a) Graph a scatter plot of the data (optional). Let x be the number of years since 1991. (b) From 1991 to 2000 the data seem to follow a linear model. Use the 1991 and 2000 points to find an equation of the line. (c) According to the linear model, in what year did the average annual cost to care for a pet ocelot seem destined to reach $900? Functions: a relationship is a function if each input has exactly one output value. Section 1.2: Determining if a Relationship is a Function 2. Determine whether the relationship is a function, and explain. {(2,10),(3,15),(4,20),(3,25)} {(3,1),(4,2),(5,1)} Function? Function? Explanation? Explanation? Worksheet 1.2: Determining if a Graph is a Function Determine which of the curves are graphs of functions. function? function? function? function? function? function? function? function? Domain and Range domain = set of values of x that are possible to plug into the equation range = set of values of y that result when you plug in x Determining the Domain The domain is either all the real numbers (domain = (-∞,∞)), or is restricted – either by context or by the impossibility of plugging in some values. There are exactly two reasons why it would be impossible to plug in a value of x: you can’t take the square root of a negative number you can’t divide by 0 Section 1.2: Determining the Domain of a Function from Its Equation Find the domain of the function, and describe the domain using interval notation. 8 1. f x 7 x 4 3. f x x 4 2. f x x 4. f x 2 1 2x 5. f x 6 x 6. f x x4 Section 1.2: Determining the Domain and Range from a Graph Describe the domain and range of each graph using interval notation. (a) domain: (a) domain: (a) domain: (a) domain: (b) range: (b) range: (a) range: (b) range: