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![Page 1: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/1.jpg)
Domain and Range: GraphDomain-
Look horizontally: What x-values are contained in the graph? That’s your domain!Range-Look vertically: What y-values are contained in the graph? That’s your range!
![Page 2: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/2.jpg)
Domain and Range: Graph
![Page 3: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/3.jpg)
Domain: [-3,2]
Range: [-5, 2]
![Page 4: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/4.jpg)
Domain and Range: Graph
![Page 5: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/5.jpg)
Domain: [-3,3)
Range: (-1, 2]
![Page 6: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/6.jpg)
Maximum and MinimumMaximum value: the highest y value seen in the data or on the graph.
Minimum value: the lowest y value seen in the data or on the graph.
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Max and Min: Graph
![Page 8: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/8.jpg)
Max: 2
Min: -5
![Page 9: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/9.jpg)
Zeros: Graph
![Page 10: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/10.jpg)
Zeros: -3; -1.2; 2
![Page 11: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/11.jpg)
Increasing and Decreasing: Graph
To find where the graph is increasing and decreasing trace the graph with your finger from left to right. Specify x-values! If your finger is going up, the graph is increasing.If your finger is going down, the graph is decreasing.
![Page 12: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/12.jpg)
Increasing and Decreasing
![Page 13: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/13.jpg)
Inc: (-3,-2.1); (.9,2.1)
Dec: (-2.1,.9)
![Page 14: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/14.jpg)
Increasing and Decreasing
∞-∞
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: ( , .5)Dec
: ( .5, )Inc
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End Behavior: Graph
The value a function, f(x), approaches when x is extremely large (∞) (to the right) or when x is extremely small (-∞) (to the left).
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End Behavior
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, ( ), ( )
x f xx f x
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End Behavior
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, ( ), ( )
x f xx f x
![Page 21: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/21.jpg)
Points of Discontinuity• These are the points where the function either “jumps” up or
down or where the function has a “hole”.• For example, in a previous example
Has a point of discontinuity at x=1
The step function also has points of discontinuity at x=1, x=2 and x=3.
![Page 22: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/22.jpg)
Maxima and Minima(aka extrema)
In this function, the minimum is at y = 1
In this function, the minimum is at y = -2
Highest point on the graph
Lowest point on the graph
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Axis of Symmetry• The vertical line that splits the equation in half.
For the equation the axis of symmetry is located at x = 1
1 1y x
This ‘axis of symmetry’ can be found by identifying the x-coordinate of the vertex (h,k), so the equation for the axis of symmetry would be x = h.
![Page 24: Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? Thats your domain! Range- Look vertically: What y-values.](https://reader034.fdocuments.us/reader034/viewer/2022050722/5a4d1b927f8b9ab0599c1b18/html5/thumbnails/24.jpg)
Intervals of Increase and Decrease• By looking at the graph of a piecewise
function, we can also see where its slope is increasing (uphill), where its slope is decreasing (downhill) and where it is constant (straight line). We use the domain to define the ‘interval’.
This function is decreasing on the interval x < -2, is Increasing on the interval -2 < x < 1, and constant over x > 1