1. MAT 1033C – INTERMEDIATE ALGEBRA
Liudmila Kashirskaya

2. 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}

3. 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.

4. 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

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

6. 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

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

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

9. 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

10. Discussion: Where the graph represents a function?

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

12. This is the function!