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Guiding Question: How can a function enhance interpretation of change?
the Anatomy of a function
the Anatomy of a function
Variables as Change: A variable (x or y) represents a quantity that can change.
Independent vs. Dependent Variables:
Independent Variable (x): The variable that "starts" the change or happens on its own (often Time).
Dependent Variable (y): The variable that "responds." Its value depends on what happens to the independent variable.
Example: If you get paid $15 per hour, the Hours are independent (x), and the Total Pay is dependent (y) because your pay depends on how many hours you work.
The Golden Rule of Functions: For every input (x), there is exactly one output (y).
representations of functions
representations of functions
There are four ways to show the same function. Being able to "translate" between them is a key Grade 6 skill.
In Words
In Words
"The total cost is five dollars times the number of tickets."
table of values
table of values
The first column is always the Independent Variable (x).
The second column is always the Dependent Variable (y).
cartesian plane
cartesian plane
The x-axis represents the independent variable.
The y-axis represents the dependent variable.
Each row in your table becomes a coordinate (x, y) on the graph.
algebraic equation
algebraic equation
Example: y = 5x (where y is cost and x is tickets).
procedures: how to "solve" a function
procedures: how to "solve" a function
Finding the Rule: Look at the table of values. What do you have to do to x to get y? Does it work for every single row?
Predicting the Future (finding y): If your rule is y = 2x + 10, and you are told x = 5, just plug it in!
(2 x 5 + 10 = 20)
Finding the Start (finding x): Use your algebra skills! If y = 20, and the rule is y = 4x, then 20 = 4x, so x must be 5.
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