exam_1_study_guide - Exam 1 Study Guide This resource is...

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Exam 1 Study Guide This resource is designed to help you focus your studying. Along the way I will try and give some helpful hints. Understand that these hints are only a small portion of what needs to be studied, and if the guide suggests you should understand something for the exam, please try to understand it. Without further ado. . . 1.2 Variables, Parameters, and Functions Understand that a variable changes throughout an experiment (or within an equation), and that a parameter remains constant throughout the experiment (or during one in- stance of solving an equation). A parameter may be modified, and you may be asked to re-examine the equation. A function is a 1-input 1-output relation (it passes the vertical line test). If the function never takes on the same function values for different input values (passes the horizontal line test) then it is invertible. Understand how to find the inverse (do not change variables! just rewrite the equation in terms of the other variable, if possible. ie, the inverse of f ( x ) would be x ( f )). Composition f g ( x ) is a means of combining two functions. Understand how to compose functions, the fact that f g ( x ) = g f ( x ), and that generally a composition only makes sense one way (think of the dimensions of the two functions). 1.3 Units and Dimensions Know how to use conversion factors to convert between different units. Know that converting between dimensions requires a special formula dependent on the situation. Be able to use such a formula. Know how to compose such formulas in order to change the input accepted by a certain function (ie. if you have mass as a function of temperature, temperature as a function of volume, and volume as a function of age, find mass as a function of age). Know in what ways changing units alters the graph of a function, and be familiar with the four methods of changing a function (horizontal and vertical shifting and scaling). Remember that horizontal shifting may not be intuitive for you, so try and refine your intuition until it makes sense.
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