Math_41_Exam_1_Review - Math 41 Exam 1 Review 1.1 Lines in...


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Math 41 Exam 1 Review 1.1 Lines in the Plane- You need to be able to find the slope of a line using two points as reference. 2 1 2 1 2 1 , . y y m x x x x Remember that a horizontal line has a slope of 0, and a vertical line has an undefined slope. You need to know the 2 forms for the equation of a line: Point-Slope Form and Slope-Intercept Form. Which form you use depends on what information you are given in the problem. If you are given two points, or a point and the slope, use Point-Slope Form. If you are given the slope and the y-intercept, use Slope- Intercept Form. You can go from Point-Slope Form to Slope-Intercept Form by solving for y. Two lines are parallel iff their slopes are equal. Two lines are perpendicular iff their slopes are negative reciprocals of each other. You need to be able to use this information to write the equations of parallel or perpendicular lines to a given line through a point. 1.2 Functions - Recall the definition of a function: A function f from a set A to a set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs, or set of x-values), and the set B is the range (or set of outputs, or set of y-values). We can represent functions using tables, ordered pairs, graphs, or equations. In functions, x is the independent variable, and y is the dependent variable. When using equations to represent functions, we usually use function notation (use f(x) instead of y). This makes it easier to plug values in for x and f(x). You need to be comfortable plugging in numbers, variables, and variable expressions into functions. You should get used to using parentheses when plugging in values in to functions. A piecewise-defined function is a function that has two or more equations defined over a specified domain. The equation that you use depends on what x-value you are plugging in. One of the most important concepts in this section, and in following sections is the concept of domain. The implied domain is the set of all real numbers for which the expression is defined. You want to look to see where the function is undefined so you can restrict your domain. Good places to look are fractions and radicals! Phrase your domain so that it includes all values that make the function defined, and then exclude values that make the function undefined. Remember that you can have a zero under a radical, unless it’s also in the denominator. When in doubt, pick values in
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