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Published byLouisa Farmer Modified over 6 years ago
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P.1 Graphs and Models Sketch the graph of an equation.
Find the intercepts of a graph. Test a graph for symmetry wrt an axis and the origin. Find the points of intersection of 2 graphs. Interpret mathematical models for real-life data.
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The Graph of an Equation
Solve 3x + y = 7. This equation has many solutions. The set of all solution points is the graph of the equation.
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Sketch a Graph by Point Plotting
It is the most basic procedure --- but has a BIG shortfall: plotting too few points might NOT represent the actual graph. (antidote: have a working knowledge of the graphs of different types of functions.) Disadvantage of using technology
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Intercepts of a graph These are solutions of the form (a,0) and (0,b).
To find the x-intercept a, set y to zero. To find the y-intercept b, set x to zero.
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Symmetry of a Graph This is a good aid in graphing (besides point-plotting). 3 types: a) y-axis symmetry: if (x, y) is a point in the graph, so is (-x, y). b) x-axis symmetry: if (x,y) is a point in the graph, so is (x, -y). c) origin: if (x,y) is a point in the graph, so is (-x, -y).
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Points of Intersection
A point of intersection of the graphs of 2 equations, also known as a system, is a point that satisfies both equations. Such a point is called a solution of the system. To find points of intersection, either graph the 2 equations in the same plane, or solve the system algebraically by substitution.
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Mathematical Models One of the end goals of mathematics: usefulness.
Aim for simplicity and accuracy: simple enough to be workable but accurate enough to produce meaningful results.
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