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2. Chapter 9
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3. Functions A function describes how a dependent variable
changes with respect to one or more
independent variables. When there are only two
variables, we often summarize them as an
ordered pair with the independent variable first:
(independent variable, dependent variable)
We say that the dependent variable is a function
of the independent variable. If x is the independent
variable and y is the dependent variable, we write the
function as y = f(x)
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4. Representing Functions
9-A
Representing Functions
There are three basic ways to represent functions.
Data Table
Draw a picture or graph
Write an equation
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5. Domain and Range The domain of a function is the set of values
that both make sense and are of interest for the
independent variable.
The range of a function consists of the values
of the dependent variable that correspond to the
values in the domain.
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6. Hours of Daylight as a Function
Here is a simple example of a periodic function that could be used as an introduction into the concepts of domain, range, independent and dependent variables.
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7. 9-B
Linear Functions
Walk through with your class several practical examples the four types of slope (positive, negative, zero, undefined). One motto for linear applications: “Don’t give up hope, find the slope!”
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8. Slope-Intercept Form of a Line
9-B
Slope-Intercept Form of a Line
y = mx + b
y = 3x – 7
refers to a line whose slope is equal to 3 and a y-intercept of -7.
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9. Exponential Functions
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10. Two Ways to Describe Exponentials
Remind students that Q(sub-not) is simply the initial value and Q is the new value that we referred to back in Chapter 8.
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11. Changing Rates of Change
The thinking about box on (page 534) is a great way to help students at least have a rough appreciation and understanding for the underpinnings of the calculus.
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