Problem 1 Interpreting a Graph
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What are the domain, period, range, and amplitude of the cosine function?
The domain of the function is all real numbers.
The function goes from its maximum value of 1 to its minimum value of
The range of the function is
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Examine the cycle of the cosine function in the interval from 0 to 2π. Where in the cycle does the maximum value occur? Where does the minimum occur? Where do the zeros occur?
The maximum value occurs at 0 and 2π. The minimum value occurs at π. The zeros occur at
Think
How do you find a zero of a function?
Zeros are where the graph of a function crosses the x-axis.
✓ Got It?
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Use the graph. What are the domain, period, range, and amplitude of the sine function? Where do the maximum and minimum values occur? Where do the zeros occur?
Take Note Concept Summary: Properties of Cosine Functions
Suppose
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- b is the number of cycles in the interval from 0 to 2π.
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To graph a cosine function, locate five points equally spaced through one cycle. For
Problem 2 Sketching the Graph of a Cosine Function
Sketch one cycle of
Divide the period into fourths. Plot the five-point pattern for one cycle. Use 1.5 for the maximum and
Plan
What should you find to graph the function?
Find the amplitude, cycle, and period.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions