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Characteristics of Functions
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Intercepts x-intercept – the point at which the line intersects the x-axis at (x, 0) y-intercept – the point at which the line intersects the y-axis at (0, y)
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Finding the Intercepts
On a graph, just look at where the function is crossing the x-axis, and then the y-axis. If you are given the equation: Plug in 0 for y and solve for x: this is the x intercept Plug in 0 for x and solve for y: this is the y intercept -3x + 2y = 12
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Interval Notation Represents an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included
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Trend of the Graph Sweep from left to right and notice what happens to the y-values Increasing goes up (L to R) Decreasing falls down (L to R) Constant is a horizontal graph
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Continuous Data -has NO breaks & is measured
-is data that can take any value (within a range) Examples: A person's height: could be any value (within the range of human heights), not just certain fixed heights; Time in a race: you could even measure it to fractions of a second
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Discrete Data -has gaps or breaks & is counted
-can only take certain values Example: the number of students in a class (you can't have half a student).
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Extrema Minimum Point – least value of the function Maximum Point –greatest value of the function
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Set Notation Using inequalities to describe the values
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Domain & Range Domain – all x-values of a function
Range – all y-values of a function
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Asymptote A line that a graph gets closer and closer to, but never crosses or touches
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The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home. What do the horizontal lines on the graph represent? Where in the graph shows her taking care of the 2 errands? Compare how she traveled at the beginning to how she traveled at the very end. Create Maria’s story so that it matches the graph.
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Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?
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Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum?
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Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum? Horizontal Asymptote:
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Characteristics Domain: Range: Intercepts: Increasing or Decreasing?
Maximum or Minimum? Horizontal Asymptote:
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Characteristics of Functions
Homework Characteristics of Functions
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