graphs of functions graphs of functions. 43210 in addition to level 3.0 and beyond what was taught...
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Graphs of Functions
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4 3 2 1 0In addition to level 3.0 and beyond what was taught in class, the student may: Make
connection with other concepts in math.
Make connection with other content areas.
The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables. Compare
properties of a function to a non-function.
The student will be able to model and evaluate functions and non-functions. Use graphs,
equations, and tables to determine functions and non-functions.
With help from theteacher, the student has partial success with level 2 and 3 elements.
Even with help, students have no success with the functions.
Focus 6 - Learning Goal #1: Students will understand and explain the difference between functions and non-functions using graphs, equations, and tables.
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A function is a rule that relates two quantities so that each input value corresponds to exactly one output value.
Define-
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In order for a graph to be a function, each x can only have ONE y.
Give an example of why this graph is not a function.
Is this graph a function? Why or why not?
Yes, each x input has only one y output.
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Is this graph a function? Why or why not?
NO, each x input has more than one y output.
Is this graph a function? Why or why not?
Yes, each x input has only one y output.
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Vertical Line Test
When looking at a graph, you can tell if a drawing is a function if it passes the vertical line test.
This means you can draw a vertical line and it will only touch the drawing (graphed figure) one time.
If it touches the drawing (graphed figure)
more than once, it is not a function.
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Determine if the relationship represents a function. Does it pass the vertical line test?
The relationship is not a function.
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Determine if the relationship represents a function. Does it pass the vertical line test?
The relationship is a function.
x
y
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Determine if the relationship represents a function. Does it pass the vertical line test?
The relationship is a function.
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Parts of a graph… Increase – A function is
“increasing” when the y-value increases as the x-value increases.
Interval – A section of the graph. ◦ This function is increasing for the
interval shown. It may be increasing or decreasing elsewhere.
Decrease – A function is “decreasing” when the y-value decreases as the x-value increases.
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Parts of a graph…
Linear: A function is linear when it makes a straight line.
*Each part of this graph is linear because each section is a straight line.
Non-Linear: A function is non-linear when it is curved.
*Each part of this graph is non-linear because each section is curved.
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At what intervals is this function increasing?
Intervals are written in between brackets [ ].
1. [0.5, 1] This means it is increasing from 0.5 to 1 along the x-axis.
2. [2, 3]This means it is increasing from 2 to 3 along the x-axis.
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At what intervals is this function decreasing?
1. [-1, 0.5] This means it is decreasing from -1 to 0.5 along the x-axis.
2. [1, 2]This means it is decreasing from 1 to 2 along the x-axis.
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At what intervals is this function linear?
1. [-1, 0] This means it is linear from -1 to 0 along the x-axis.
2. [1, 2]This means it is linear from 1 to 2 along the x-axis.
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At what intervals is this function non-linear?
1. [0, 1] This means it is non-linear from 0 to 1 along the x-axis.
2. [2, 3]This means it is decreasing from 2 to 3 along the x-axis.