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Review Math 140Exam 1. Explain what a variable is and make the distinction between independent and dependent variables. Define a function by a table,

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Presentation on theme: "Review Math 140Exam 1. Explain what a variable is and make the distinction between independent and dependent variables. Define a function by a table,"— Presentation transcript:

1 Review Math 140Exam 1

2 Explain what a variable is and make the distinction between independent and dependent variables. Define a function by a table, a graph, a rule, or a set of ordered pairs. The rule is often given by an algebraic formula. Use function notation, such as writing an expression for g(t+2) given a formula for g. Read information, such as domain, range and function values from a graph. Distinguish between the domain/range of an abstract function and the domain/range of a function used as a model. Distinguish between discrete and continuous variables. Determine whether or not a given relationship is a function. For a function with a constant rate of change, figure out that rate from its graph, table, or formula. Compute the average rate of change of any function between two points. Describe the curvature of the graph of a function. Draw a reasonably accurate graph of a relationship based on info supplied. Progress Check Chapter 1

3 Recognize linear and exponential functions from their formulas. Write a formula for a linear function, given two points, or any one point and the constant rate of change. Use appropriate units for the slope of a linear model. Recognize and write equations for horizontal and vertical lines. Write a formula for an exponential function, given its y intercept and constant growth factor. Given two values of an exponential function, calculate the growth factor. Given a graph, write a formula for a linear, piecewise linear, or exponential function. Graph a piecewise function, given its formula or a description of its rule. Explain the difference between the domain/range of an abstract function and the domain/range of a function used as a model. Chapter 2 Progress Check

4 Chapter 3 Recognize a graph as belonging to one of the function families whose portraits appear in the introduction. Determine precisely how modifications to a function will affect its graph. Recognize even or odd functions by graph or formula Find the algebraic formula for the composition of two functions. Work backward from a composite function to find simpler functions that produced it. Determine the domain of a composite function. Determine from a graph whether it is one-to-one and thus has an inverse. Given the graph of a one-to-one function, sketch the graph of the inverse function. Given algebraic formulas for two functions, test whether or not they are inverses. Find the algebraic formula for the inverse of a function. Know the relationship between domain/range of a function and domain/range of its inverse. Progress Check

5 f(x) + cAdd constant to outputGraph up (c>0) Graph down (c<0) f(x+c)Add constant to inputGraph left (c>0) Graph right (c<0) -f(x)Opposite outputGraph reflects about x-axis f(-x)Opposite inputGraph reflects about y-axis c*f(x)Multiply output by a constantVertically stretch by c. f(c*x)Multiply input by constantHorizontal stretch by 1/c f( lxl )Absolute value of input? l f(x) lAbsolute value of output? Project 3.4 pages 144-5


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