Algebra 1-2

Unit3Notes

Any relationship between two variables is called a ______
A function is a rule that establishes a relationship between two quantities, called the
______and the ______.

FUNCTIONS:
  • For each input, there is exactly one output (there can be no repetition of input values).
  • For each output, there can be more than one input (there can be a repetition of output values).
  • Another way to describe the function above is by using ordered pairs.
{(0, 0), (1, 5), (2, 10), (3, 15)}
  • Another way to describe the function above is by using an input-output table:
Input
Output
The collection of all input values is called the ______of the function. This can also be described as the set of all the ____ values.
The collection of all output values is the ______of the function. This can also be described as the set of all the ____ values.
The variable graphed on the horizontal axis is the ______variable. This corresponds to the ______values.
The variable graphed on vertical axis is the ______variable. This corresponds to the ______values.
Example 1: Decide whether the relation is a function. State the domain and range. Rewrite each relationship as a set of ordered pairs.
a.) Input Output




/ b.) Input Output
Example 2: Does the table represent a function? Explain. State the domain and range.
a.)
Input / Output
1 / 3
2 / 3
3 / 4
4 / 5
/ b.)
Input / 1 / 1 / 2 / 3
Output / 3 / 4 / 5 / 6
Example 3: Does the set of ordered pairs represent a function? Explain. State the domain and range.
a.) {(-2, 5), (3, -7), (1, 8), (0, 2)} / b.) {(5, 2), (-3, 10), (2, -4), (-3, 7), (-5, -2)}
c.) {(1, -8), (2, -8), (3, -8), (4, -8), (5, -8)} / d.) {(5, 5), (-1, 4), (5, -8), (5, -3)}
Example 4: Make an input-output table for the function.
a.) y = 2x + 1
Input / Output
/ b.) y = -6x + 2
Input
Output
.
VERTICAL LINE TEST
  • The vertical line test helps you determine if a relation is a function. If all possible vertical lines cross the graph only once or not at all, then the graph represents a function.
  • The graph does not represent a function if you can draw even one vertical line that crosses the graph two or more times.

Example 5: Use the VLT to determine if the relation a function?
1.
/ 2.
/ 3.

4.
/ 5.
/ 6.

7.
/ 8.
/ 9.

Go back and decide whether the graphs represent continuous or discrete functions.
FUNCTION NOTATION
  • When a function is defined by an equation, it is convenient to give the function a name.
  • In general, the symbol f (x) replaces y and is read “the value of f of x,” or simply as “f of x.” It does not mean f times x.
  • f (x) is called function notation.
  • f (x), g(x) and h(x)are commonly used function names.

Example 6 – Find each unknown function value or x-value for f(x) = 4x – 7 and g(x) = -3x + 5.
a. f(2) / b. f(0) / c. g(-7)
d. x, when f(x) = -3 / e. g(6) / f. x, when g(x) = 5
Example 7 – You can use the function f(x) = x + 32 to find the temperature f(x) in degrees Fahrenheit for any given temperature x in degrees Celsius. Find the specified value.
a. f(15) / b. f(-10)
c. x when f(x) = 41 / d. x when f(x) = -4

Try These

1. Tell whether each table represents a function. State the domain and range.
A.

B.

C.

2. Each graph below represents a relation. Use the vertical line test to determine if the relations is
a function.
A.
/ B.

C.
/ D.

4. Tell whether each set of ordered pairs represents a function. State the domain and range.
a.) {(9, 3), (-4, -1), (0, -9), (-4, -2)} / b.) {(7, -8), (7, 4), (7, 0), (7, -11), (7, -5)}
c.) {(-5, 3), (-4, -2), (-3, 3), (-2, -2), (-1, 3)} / d.) {(-6, 8), (2, -1), (4, 0), (-1, -3)}
5. You join an aerobics class at the local gym. The cost is $1 per class plus $3 for the initial membership fee.
a.) Write an equation that shows the relationship between the number of classes x you attend and the amount you pay y.
b.) Evaluate the equation for x = 1, 2, 5, and 7. Organize your results in an input-output table.
Input / Output
c.) Draw a line graph to represent the data in the input-output table.

d.) The vertical line test can be used to see if a relation is a function
e.) Write the equation in function notation.