M1: Analyzing Functions Flashcards
Write an equation representing the linear function that includes the points given?
( -1, 7.5 ), ( 2, 6 ), ( 5, 4.5 ), ( 8, 3 )
y = - 1/2x + 7
What is Domain?
y=|x|
Domain Is:
How far the x-values go left and right.
Domain:
(-∞, +∞)
Explanation:
The reason why the domain is (-∞, +∞) is because the farthest x-value to the left is going on infinitely, and the farthest x-value to the right is also going infinitely.
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What is the Range?
y = |x|
Range Is:
How far the y-values go up and down.
Range:
[0,∞)
Explanation:
The reason why the range is [0,∞) is because the absolute value equation start at y=0 and goes up +∞. If the equation was making the graph open downwards, it would be [0,-∞).
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What is End Behavior?
y= 2|x-12|
End Behavior is:
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
End Behavior:
x -> -oo; y -> +oo
x -> +oo; y -> +oo
Explanation:
The reason why that is the End Behavior, is because on the left end of the vertex, the x value approaches -oo and the y value approaches +oo because the arrow is pointing up while going left. On the right end of the vertex, the x value approaches +oo and the y value approaches +oo because the arrow is pointing up while going right.
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What is the Increasing Interval?
Increasing Interval is:
The graph of a function that is increasing on an interval rises from left to right on that interval
(or the point where the graph starts going up)
What is the Decreasing Interval?
Decreasing Interval is:
Where the line is going down (decreasing slope) on the graph.
What is the maximum?
Maximum is:
The top most point of the line.
What is the minimum?
Minimum is:
The bottom most point of the line.
What are turning points?
Turning Point is:
A function may change from increasing to decreasing or vice versa.
What are zeros?
Zeros are:
The point at which the graph crosses the x-axis
What is a relation?
Relations are:
A general term for any set of order pairs.
What is a function?
Functions are:
When x’s aren’t allowed to repeat but y’s are allowed to repeat.
What is a linear function ?
Linear Function is:
Any function that graphs to a straight line. What this means mathematically is that the function has either one or two variables with no exponents or powers. If the function has more variables, the variables must be constants or known variables for the function to remain a linear function.
