TS: Making decisions after reflection and review Functions TS: Making decisions after reflection and review Warm-Up: Given f(x) = 2x – 3 what is f(-2)? What about 3f(-2)?

Objectives To determine if a relation is a function. To use the vertical line test to decide whether an equation defines a function. To find the domain and range of a function. To use function notation to evaluate functions.

Vocabulary A relation is a set of ordered pairs. { (1, 2), (2, 4), (3, 6) } The domain of a relation is the set of 1st elements. (x’s) { 1, 2, 3 } The range of a relation is the set of 2nd elements. (y’s) { 2, 4, 6 }

Functions A function is a machine.

Functions You put something in.

Functions Information is processed.

Functions You get something out.

Functions A function is a relation in which every element in the domain is paired with exactly one element in the range. PEOPLE Michael Tony Yvonne Justin Dylan Megan Elizabeth Emily BLOOD TYPE A B AB O

Function? D R 1 2 7 4 8 5 3 6 9 Function Function Not a Function

Function? {(1, 2), (3, 4), (5, 6), (7, 8)} Function {(1, 2), (3, 2), (5, 6), (7, 6)} {(1, 2), (1, 3), (5, 6), (5, 7)} Not a Function

Vertical Line Test If a vertical line can intersect a graph in more than one point, then the graph is not a function.

Function? Function Not a Function Domain: (-, ) Domain: [-3, 3] Range: [0, ) Range: [-3, 3]

Function? Not a Function Function Domain: [0, ) Domain: (-, ) Range: (-, ) Range: (-, )

Function? Not a Function Function Domain: (-, 0] Domain: (-, ) Range: (-, ) Range: (-, 0]

Is Y a function of X? YES! NO! YES! NO!

Functions A function pairs one object with another. A function will produce only one object for any pairing. A function can be represented by an equation.

In order to distinguish one function from another we must name it. Functions In order to distinguish one function from another we must name it.

Values that go into a function are independent. Functions Values that go into a function are independent.

Values that come out of a function are dependent. Functions Values that come out of a function are dependent.

Functions To evaluate the function for a particular value, substitute that value into the equation and solve. You can evaluate a function for an expression as well as for a number. To do so, substitute the entire expression into the equation. Be careful to include parentheses where needed.

Functions Find what y equals the machine when x equals 5. f is a function of x that produces x - squared Find f (5)

Function Notation Variable in the function Name of the function

Function Notation

Piece-wise Function

Function Notation

The Difference Quotient

The Difference Quotient

Composition Functions Given f(x) = 2x – 3 and g(x) = x2 but…

Conclusion A function is a relationship between two sets that pairs one object in the first set with one and only one object in the second set. To evaluate the function for a particular value, substitute that value into the equation and solve. To evaluate the function for an expression, substitute the entire expression into the equation; include parentheses where needed.