AP CALCULUS Review-2: Functions and their Graphs.

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Presentation transcript:

AP CALCULUS Review-2: Functions and their Graphs

Functions Def: A function is a special type of relation. y is a function of x if for each x-value there is only one y- value. The graph of a function passes the vertical line test. This is written Domain: the set of all x-values Range: the set of all y-values Notation:

Functions One-to-one Function: a function in which not only is there only one y for each x, but there is also only one x for each y. The graph passes the horizontal line test as well as the vertical line test.

Find the domain and range 1.

Find the domain and range 2.

Functions are commonly represented 4 ways Verbally: by a sentence that describes the relationship between variables Numerically: by a table or list of ordered pairs Graphically: by points on a coordinate plane Analytically: by an equation in two variables

Find x-intercepts and the y-intercepts 3.

Piecewise Functions Piecewise Function: a function defined differently on different pieces of its domain. Example:

Piecewise Functions 4. Find the domain and range for

Parent Graphs a) Constant function b) Cubic Function

Graph 5. what is the transformation?

Behavior of a graph If a graph is continuous it has No breaks, holes or asymptotes

Leading coefficient Test In the polynomial function Where the a, b, and c values are coefficients and a is the leading coefficient If a is not zero then n is the degree of the polynomial

End Behavior is determined by the degree a.Even degree b.Odd degree c.Notation for end behavior

6. Is the polynomial even or odd?

7. Graph and Describe the end behavior of the graph

8) Graph and describe the end behavior

9. Find the discontinuity, then graph

Additional exercises Review Assignment 2 Problems # 10-14