5.4 - Analyzing Graphs of Polynomial Functions

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Presentation transcript:

5.4 - Analyzing Graphs of Polynomial Functions

Example 1: Graph f(x) = –x3 – 4x2 + 5 by making a table of values.

Location Principle:

Example 2: Determine consecutive values of x between which each real zero of the function is located. Then draw the graph. f(x) = x4 – x3 – 4x2 + 1

Maximum & Minimum Points Relative Maximum – a point on the graph of a function where no other nearby points have a greater y-coordinate. Relative Minimum - a point on the graph of a function where no other nearby points have a lesser y-coordinate.

Maximum & Minimum Points Extrema – max. and min. values of a function. Turning Point – when the graph turns. Another name for relative max. and min. - The graph of a polynomial function of degree n has at most n – 1 turning points.

Find Extrema on Calculator: Enter equation into y =. 2nd Calc Choose 3: minimum or 4: maximum. Curser on left of min/max, enter. Curser on right of min/max, enter. Enter.

Example 3: Graph f(x) = -2x3 + 4x2 + 5. Find the zeros of the function and relative extrema.

Example 4: Consider the graph of f(x) = x3 + 2x2 + 7. Estimate where the relative extrema occur and find the zeros.

Example 5: A) Find the domain and range B) Find the least possible degree