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Intro to Functions
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What you will learn from this videoWhat you will learn
- We’ll learn that a function is a special type of equation in which one input produces one output.
- We will also learn how to identify functions from graphs and data tables.
- And we’ll see that this knowledge can help us juice sugarcane, get carnival tokens, and make tasty treats!
- Discussion Questions
Before Video
What is a relation?ANSWERA relation is any rule that connects two variables. A relation can connect both quantitative and qualitative variables
A variable is a placeholder for an unknown measurement. Since measuring is the act of sizing attributes, a variable represents an unknown aspect of an attribute.
Relations are important because they help us describe relationships between two values or concepts. They allow us to define, discuss, and use relationships between variables in problem-solving.
I can represent a relation verbally, in a table of values, as a set of ordered pairs, and as an equation.
A linear relation forms a straight line. The equation of a linear relation has a rate and a constant, and it can be represented as y=mx+b.
After Video
What is the difference between a relation and a function?ANSWERA function is a relation where each input produces only one output.
Function notation makes it easier to see the input and output in a function. Function notation says f(input)=output, which makes it easy to write the ordered pair (input, output), and easy to graph, since the input is on the x-axis and the output is on the y-axis.
A linear function has a graph that is a straight line. The function increases to the right if it has a positive slope (rate) and decreases if it has a negative slope (rate).
A function is non-linear if its graph is not a straight line. Some examples of non-linear functions are quadratic and cubic functions.
The vertical line test is a method for determining if a relation is a function using its graph on a coordinate plane. Imagine drawing a vertical line on the coordinate plane and scanning it from left to right. If at any point the vertical line would cross the relation in two or more places, the relation fails the vertical line test, so it is not a function.
- Vocabulary
- Function DEFINE
A relation that takes an input and gives one output. We can represent functions with a table of values, ordered pairs, a graph, an equation, function notation, or words.
- Input DEFINE
A value that we substitute into a function that is transformed by the function into the output.
- Output DEFINE
The answer given by substituting the input into the function.
- Vertical line test DEFINE
A method for determining if the graph of a relation is also a function. If a vertical line scanned from left to right on the graph only intersects the relation once at any time, the relation is also a function. If at any x-value the vertical line crosses the relation more than once, the relation is not a function.
- Relation DEFINE
Any rule that connects one variable to another. We can represent a relation with a table of values, a set of ordered pairs, a graph, an equation, or words.
- Linear function DEFINE
A function that, when graphed, forms a straight line.
- Function DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide