Independent/Dependent Variables
A movie theater chargers 8 dollars per ticket. What is the independent, what is the dependent variable?
I: number of tickets, D: total cost (dollars)
What is the domain/range of graph number 1?
Domain: (-infinity, infinity)
Range: (-infinity, infinity)
Is this relation a function?
{(1,2),(2,3),(3,4)}
Yes, every x has exactly one y
A graph goes up from left to right.
Is it increasing, decreasing, or constant? Draw it.
Increasing
Which function family forms a straight line? Draw it.
Linear
A car travels at a constant speed of 60 miles per hour. Identify the independent and dependent variable.
I: Time (hours)
D: distance traveled (miles)
What is the domain/range of graph number 2?
Domain: (-infinity, infinity)
Range: [-2, infinity)
Is this relation a function?
{(2,1),(2,4),(3,5)}
No, the x value "2" has more than one y value
A graph rises, then falls.
Which description fits best? Increasing, decreasing, constant, combination? Draw it.
Combination
Which function family creates a V-shape? Draw it.
Absolute Value
A water tank is being filled at a rate of 5 gallons per minute. What is the independent, what is the dependent variable?
I: time (minutes)
D: amount of water in tank (gallons)
What is the domain/range of the set of ordered pairs, {(1,4),(2,5),(3,6)}
domain: {1,2,3}
range: {4,5,6}
What do we use to determine if a graph is a function or not? What does this method mean?
Vertical Line Test, no matter where you draw vertical line on your coordinate plane, the vertical line will only intersect your graph exactly once if it is a function
A graph has a highest point but no lowest point.
What does the graph have? Maximum, minimum, both, neither? Draw it.
Absolute maximum
Which function family increases or decreases rapidly and never crosses the x-axis? Draw an example.
Exponential, gets very close to zero but never actually hits zero
A graph shows how many miles a person walked during a time in minutes. What would be the label for the x-axis? What would be the label for the y-axis?
x-axis: time (minutes)
y-axis: distance (miles)
What is the domain/range of the set of ordered pairs, {(−2,3),(0,3),(2,5)}
domain: {-2,0,2}
range: {3,5}
Can a relation be a function if two x values have the same y-value?
Explain.
Yes, two x values can have the same y value. Two y values WILL NOT have the same x value
A graph is symmetric across the y-axis.
What type of symmetry is this? Draw a graph with this type of symmetry.
Vertical symmetry
A graph is made of multiple line segments with different rules. Draw an example.
Linear Piecewise
A bakery makes 48 cookies every hour. What label belongs on the x-axis? What label belongs on the y-axis?
x-axis: time(hours)
y-axis: number of cookies
What is the domain/range of the mapping on the whiteboard?
domain: {-1,2,5}
range: {-5,4,5,6}
Create a graph that is not a function and explain your reasoning.
Answers may vary
A graph has no symmetry and no absolute maximum or minimum.
What can you say about the shape or behavior of the graph? Draw an example.
Which function family has vertical symmetry and forms a "U" shape? Draw an example.
Quadratic