Exam 1 review sheet - Any review sheet is a compilation of...

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Any review sheet is a compilation of personal opinions about the relative importance of various parts of the material. These are jason's. It would be crazy to rely on any single resource to study for your Exam, including this little study guide! Material covered on Exam 1: Chapter 1, sections 1.1-1.8 Chapter 2, sections 2.1-2.6 with a ``lighter'' emphasis on sections 1.7-1.8 which discuss continuity and limits. Section 1.1 -Functions, linearity, proportionality Some phrases which should give you that comfortable and confident familiar feeling: ``. ..is a function of. ..'', ``is not a function of,'' ``is inversely proportional to the square root of'', ``has as its domain [4,6]'', ``is not in the range of'', ``constant rate of change'', ``by a table, a graph, a formula, and a verbal description'', ``the difference quotient '', ``is decreasing for negative x '', ``find the vertical intercept'', etc. What's the domain of ? What's its range? How can you tell from a table whether a function is linear? If it is linear, how can you find its formula? How is slope related to increasingness/decreasingness of a linear function? Can you read the slope from a graph? Can you read the y -intercept? What's a constant of proportionality, and why might you have to use one? And if you use one, how do you usually calculate its value? How can you read domain and range from a graph? What does the Greek capital Delta mean? Section 1.2 -Exponentials Exponential functions have constant what? Here's one people seem to get wrong more often than right: What's a continuous growth rate? What's a growth factor? If the growth rate is 0.5, what's the growth factor? Which one appears on the general formula and which one appears in ? Speaking of these two, why do we have two formulas for an exponential function? If I give you one, can you convert it to the other? I like to think about this by analogy with the two forms of linear functions: point-slope and slope-intersept form. What does concave-down mean? How can you see it on a graph? on a table? What's that ? Yes, yes, I know it's the initial value, but what does it represent in the context of any particular problem? How can you tell at a glance whether a formula represents exponential
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growth or decay? Write an exponential function that starts really big and decays really slowly. Can you tell from a table whether a function might be exponential? How? If it is exponential, how can you find its formula? (Careful, this is really easy in some examples, but can be hard in others!) From two points on a graph can you find the formula? It's fun to ask (ala 1.4.50) ``When will the population reach 5 million,'' or
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Exam 1 review sheet - Any review sheet is a compilation of...

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