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Analyzing Graphs AP Calculus AB Functions

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Domain & Range Domain: All x values for which a function is defined. Range: All y values for which a function is defined. implicit (i.e. implied) explicit (i.e. defined) All real numbers for which the equation is defined. Given with the function. y is the dependent variable – Its value depends on x.

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Interval Notation GraphSet NotationInterval NotationMeaning closed interval from a to b open interval from a to b half-open interval including a but not b half-open interval including b but not a closed interval from a to open interval from a to closed interval from b to -

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Intercepts The intercepts of a graph are the points at which it intersects an axis. x-intercepts: Let y = 0 and solve. y-intercepts: Let x = 0 and solve. Given, find all intercepts.

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Intersections When solving systems of 2 or more equations, the solution(s) are the intersections of the graphs. To solve algebraically use substitution or elimination. CALCULATOR TIP: Use the calculator to verify the solutions. -Enter the functions into Y=. -Go to CALC (2 nd Trace). -Choose INTERSECT (5). -Move the cursor near the intersection you want it to find. Find all points of intersection of.

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Transformations When a parent graph has been transformed, its function is altered in the following ways: f (x) parent function h (x) transformed function Vertical shift c units up Vertical shift c units down Horizontal shift c units left Horizontal shift c units right Reflection over the x-axis

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Inverses Graphically, the inverse of a function is its reflection over the line y = x. The coordinates of each point of the original function interchange to achieve a point of the inverse function.

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Vertical Asymptotes To find the vertical asymptotes of a function, set the denominator equal to zero and find all x-values for which the function is undefined. Find the vertical asymptotes of.

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Other Discontinuities Some graphs have horizontal asymptotes instead of or in addition to vertical asymptotes.

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Other Discontinuities Removable discontinuities are single points where there are holes in the graph.

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Assignment p. 8: 1-4, 15-20, 61-64 p. 27: 1, 2, 13, 14, 17, 18, 47-53, 55 p. 347: 6-12

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