Analyzing Graphs AP Calculus AB Functions. Domain & Range Domain: All x values for which a function is defined. Range: All y values for which a function.

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Presentation transcript:

Analyzing Graphs AP Calculus AB Functions

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.

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 - 

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.

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.

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

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.

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.

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

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

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