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Questions and Answers
What is the interval of decrease in the given graph?
What is the interval of decrease in the given graph?
What is a characteristic of a minimum in the graph?
What is a characteristic of a minimum in the graph?
What is the y-coordinate of the origin in the given graph?
What is the y-coordinate of the origin in the given graph?
What is the interval where the graph is horizontal?
What is the interval where the graph is horizontal?
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What is true about the given graph?
What is true about the given graph?
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What does a point on the graph marked with a dot () represent?
What does a point on the graph marked with a dot () represent?
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What is the domain of the function represented by the graph?
What is the domain of the function represented by the graph?
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What is denoted by the set of all y-values that the graph covers?
What is denoted by the set of all y-values that the graph covers?
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What is the interval of growth of the function represented by the graph?
What is the interval of growth of the function represented by the graph?
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What is the set of all x-values where the graph is above the x-axis denoted by?
What is the set of all x-values where the graph is above the x-axis denoted by?
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Study Notes
Graph of a Function
- A point on the graph marked with a dot () means the value is part of the study, and is denoted by square brackets [].
- A point on the graph not marked with a dot () means the value is not part of the study, and is denoted by parentheses ().
- The graph is always read from left to right and from bottom to top.
Domain
- The domain of a function consists of all the x-values that the function takes.
- The domain is denoted by the set of all x-values that the graph covers.
- In this case, the domain is all x-values from -∞ to 5 (not including 5), and from 7 to ∞.
Image
- The image of a function consists of all the y-values that the function takes.
- The image is denoted by the set of all y-values that the graph covers.
- To find the image, we can start from the bottom of the graph and move upwards, noting all the y-values that the graph covers.
Roots
- The roots of a function are the x-values where the graph intersects the x-axis.
- The roots are denoted by the points where the graph touches the x-axis.
- The roots can be written in various ways, such as: C(-6), C(-2), C(4) or x = -6, x = -2, x = 4.
Positivity Set
- The positivity set of a function consists of all the x-values where the graph is above the x-axis.
- The positivity set is denoted by the set of all x-values where the graph is above the x-axis.
- In this case, the positivity set is all x-values from -∞ to -6 (not including -6), and from -2 to 4 (not including 4), and from 7 to ∞.
Negativity Set
- The negativity set of a function consists of all the x-values where the graph is below the x-axis.
- The negativity set is denoted by the set of all x-values where the graph is below the x-axis.
- In this case, the negativity set is all x-values from -6 to -2 (not including -2), and from 4 to 7 (not including 7).
Interval of Growth and Decrease
- The interval of growth is where the graph is increasing, and is denoted by the green part of the graph.
- The interval of decrease is where the graph is decreasing, and is denoted by the red part of the graph.
- In this case, the interval of growth is from -4 to -1 (not including -1), and from 4 to 5 (not including 5), and from 7 to ∞.
- The interval of decrease is from -∞ to -4 (not including -4), and from -1 to 4 (not including 4).
Maximum and Minimum
- A maximum is a point where the graph changes from increasing to decreasing.
- A minimum is a point where the graph changes from decreasing to increasing.
- In this case, there are no maxima or minima.
Origin
- The origin is the point where the graph intersects the y-axis.
- The origin is denoted by the point where the graph touches the y-axis.
- In this case, the origin is at y = 2.
Constant
- A constant is an interval where the graph is horizontal, neither increasing nor decreasing.
- The constant is denoted by the part of the graph that is horizontal.
- In this case, the constant is from -1 to 2 (not including 2).
Graph of a Function
- A point on the graph marked with a dot (•) indicates the value is part of the study, denoted by square brackets [].
- A point on the graph not marked with a dot (•) indicates the value is not part of the study, denoted by parentheses ().
Domain
- The domain of a function consists of all x-values that the function takes.
- The domain is denoted by the set of all x-values that the graph covers.
Image
- The image of a function consists of all y-values that the function takes.
- The image is denoted by the set of all y-values that the graph covers.
Roots
- The roots of a function are the x-values where the graph intersects the x-axis.
- The roots are denoted by the points where the graph touches the x-axis.
Positivity Set
- The positivity set of a function consists of all x-values where the graph is above the x-axis.
Negativity Set
- The negativity set of a function consists of all x-values where the graph is below the x-axis.
Interval of Growth and Decrease
- The interval of growth is where the graph is increasing.
- The interval of decrease is where the graph is decreasing.
Maximum and Minimum
- A maximum is a point where the graph changes from increasing to decreasing.
- A minimum is a point where the graph changes from decreasing to increasing.
Origin
- The origin is the point where the graph intersects the y-axis.
Constant
- A constant is an interval where the graph is horizontal, neither increasing nor decreasing.
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Description
Learn about graphing functions, including domain and notation conventions. Understand how to read graphs and identify domain values.
