MAT 1033C – INTERMEDIATE ALGEBRA Liudmila Kashirskaya lkashirskaya@mail.valenciacollege.edu

Creating Line Graphs S={(0,-4), (1,-1,), (2,2), (3,5)} D={ 0,1,2,3} x 1 2 3 y -4 -1 5 S={(0,-4), (1,-1,), (2,2), (3,5)} D={ 0,1,2,3} R={ -4,-1,2,5}

x–independent variable, y- dependent variable. Chapter 2.1 Functions and Their Representations The notation y=f(x) is called The function notation. The input is x, the output is y, and the name of the function is f. y = f(x) x–independent variable, y- dependent variable.

Example 1: Suppose that a person works for $9 per hour Example 1: Suppose that a person works for $9 per hour. Calculate the amount of money the person earns after working x hours. Input x ---Function f ---Output y=f(x) f(x)=9x

Representing Functions 1. Verbally 2. symbolically 3. numerically 4. graphically

Verbal representation (words) Example 2: For example, the circumference of a square is four times one of its sides. Symbolic representation (formula) Example 3: Evaluate the function f at the given value of x f(x)=x2+1, x= -4, 0, 2

Numerical representation (table of values) Example 4: Yards to feet X (yards) 1 2 3 4 Y(feet)  3  6  9  12

Graphical representation( GRAPH) input is x, the output is y Each input results in exactly one output!!!

Defining a Function A function f is the set of ordered pairs (x,y), where each x-value corresponds to exactly one y-value. The domain of f –Dx, the range of f -Ry

Discussion: Where the graph represents a function?

The vertical line test: If every vertical line intersects a graph at no more than one point, then the graph represents a function.

This is the function!