functions section 8.1. notes: relations and functions the ________________ is a value that does not...
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Notes: Relations and Functions
The ________________ is a value that does not depend upon another variable.
The _________________ is a value that depends on the input value.
Recall that functions are _________ in which each element of the domain is paired with __________ one element of the range.
Examples
Determine whether each relation is a function. Explain.
1. (5,1), (6,3), (7,5), (8,0)
2. (54,112), (56,130), (55,145), (54,123), (56,128)
Notes: Relations and Functions
Another way to determine whether a relation is a function is to apply the ___________ to the graph of the function.
If, for each value of x in the domain, a vertical line passes through no more than one point on the graph, then the graph represents a function.
If the line passes through more than one point on the graph, it is not a function.
Notes: Function Notation
A function that is written as an equation can also be written in a form called ____________.
Consider the equation y = 2x + 3
Equation Function Notation
y = 2x + 3 f(x) = 2x + 3
Notes: Function Notation
The variable y and f(x) both represent the _________ variable.
In the example above, when x = ____, f(x) = ____
In function notation, f(x) is read “f of x” and is equal to the value of the function at x.
Notes: Describe Relationships
A function can also describe the relationship between two quantities.
For example, the distant you travel in a car depends on how long you are in he car.
In other words, distance is a function of time or d(t)
Example 1. A whale watching boat traveled at a sped of 5.5 miles
per hour.
A. Identify the independent and dependent variables. Then write a function to represent the total distance traveled in any number of hours spent whale watching.
B. Use the function to find how long it took to travel 25 miles. Round to the nearest tenth.
H.O.T. Problems
38. Draw two graphs, one that represents a relation that is a function and one that represents a relation that is not a function. Explain why each graph is or is not a function.