Tables & Ordered Pairs
In the ordered pair (3, 7), what is the input, or x value?
3
What is a function?
A relation in which every input has exactly one output.
What test can you use to determine whether a graph represents a function?
The vertical line test.
What is the domain of the relation (1, 4), (2, 5), (3, 6)?
{1, 2, 3}
FOOD: What is the only food that never spoils when stored properly and sealed?
Honey
A relation contains the ordered pairs (1, 4), (2, 5), (3, 6). What is the output when the input is 2?
5
Is the relation y=x+3 a function?
Yes. y=mx+b! Every input x produces exactly one output y.
A graph is a straight horizontal line at y=4. Does it represent a function?
Yes. Each vertical line intersects the graph at most once.
What is the range of the relation (2, 7), (4, 9), (6, 11)?
{7, 9, 11}
HOLIDAY: What November holiday is celebrated in Mexico on November 1 and 2?
Día de los Muertos (Day of the Dead).
Is this relation a function? Explain why or why not.
(1, 3), (2, 5), (1, 7)
No. The input 1 has two different outputs, 3 and 7.
Is this relation a function? (2, 5), (4, 5), (6, 5)
Yes! Each input has exactly one output, even though the outputs are the same.
A graph contains the points (1, 2), (2, 4), and (3, 6). Does it represent a function?
Yes. No input x is paired with more than one output y.
A student buys notebooks for $3 each. The total cost depends on the number of notebooks purchased. Identify the independent and dependent variables.
Independent: number of notebooks.
Dependent: total cost.
SPORTS: A team scores a touchdown, kicks the extra point, and then scores a field goal. How many total points did the team score?
10 points (6 + 1 + 3)
A table shows the following values:
x 2 3 4 3
y 4 6 8 9
No. The input 3 has two different outputs, 6 and 9.
A relation maps input 1 to output 4, input 2 to output 6, and input 3 to both outputs 7 and 8. Is it a function? Why?
No! Input 3 has two different outputs.
A graph is a circle. Does it represent a function?
No. Some vertical lines intersect the circle twice, meaning one input has two outputs.
Find the domain and range of the relation (-1, 3), (0, 5), (2, 3), (4, 7).
Domain: {-1, 0, 2, 4}. Range: {3, 5, 7}.
HISTORY: What major historical event ended on November 11, 1918, inspiring the date of Veterans Day?
World War I (the armistice took effect at the 11th hour of the 11th day of the 11th month).
A function contains the ordered pairs (-2, 4), (0, 1), (2, 4), (5, 7). Can two different inputs have the same output in a function? Use this relation to explain.
Yes. The inputs −2 and 2 both have the output 4. This is allowed because each input has exactly one output.
A student says, “A relation is not a function if two ordered pairs have the same y-value.” Is the student correct? Explain.
No. Different inputs may have the same output. A relation fails to be a function only when an input has more than one output.
A graph passes the vertical line test. Is the relation a function?
Yes! Every input x has exactly one output y.
What is Domain of the relation (0,1) (2,2) (4,3) (0,4) (1,5) (3,6)
{0,1,2,3,4}
SCIENCE: What causes many leaves to change color in the fall?
As daylight decreases and temperatures change, trees break down chlorophyll, revealing other colors in the leaves.