3.3 Rates of Change

• In the formula for the rate of change, Δy represents the change in the y-variable.
• If a car travels 120 miles in 2 hours, what is its average speed (rate of change)?

  60 miles per hour
• What is the definition of a dependent variable?

  Measured and observed
• The number of study hours is an example of an independent variable.


  True
• What is the formula for calculating the average rate of change?

  (y₂ - y₁) / (x₂ - x₁)
• The average rate of change from x = 1 to x = 3 in the given example is 3 degrees per hour.

  True
• What is the rate of change from time 0 to 2 in the given example?

  2 degrees per hour
• What is the definition of an independent variable?

  The variable that is manipulated
• Give an example of a real-life relationship where the number of hours studied is the independent variable.

  Exam score
• The independent variable is defined as the variable that is manipulated or changed
• What is the dependent variable in a relationship between two variables?

  The variable that is measured
• The dependent variable is positioned on the y-axis of a graph.


  True
• The formula for average rate of change is (y₂ - y₁) / (x₂ - x₁
• How does the instantaneous rate of change differ from the average rate of change?

  Measures change at a specific moment
• The instantaneous rate of change is calculated using two data points.

  False
• The formula for rate of change is Δy / Δx
• What is the independent variable in a relationship between two variables?

  The variable that is manipulated
• The independent variable is the effect in a cause-effect relationship.

  False
• In a graph, the independent variable is positioned on the X-axis
• The average rate of change is calculated using the formula (y₂ - y₁) / (x₂ - x₁)
• Steps to calculate the average rate of change

  1️⃣ Identify the starting and ending x-values

  2️⃣ Identify the corresponding starting and ending y-values

  3️⃣ Apply the average rate of change formula

  4️⃣ Simplify the result
• The instantaneous rate of change is the slope of the tangent line at a specific point on the graph of the function.
• The instantaneous rate of change is more precise than the average rate of change.


  True
• In real life, speed is measured as distance traveled per unit of time
• If a car travels 120 miles in 2 hours, its average speed is 60 miles per hour.


  True
• What is the formula to calculate the rate of change?

  Rate of change = Δy / Δx
• The rate of change from time 0 to 2 in the given example is 2 degrees per hour.

  True
• Arrange the steps to identify independent and dependent variables.

  1️⃣ Define the relationship between variables

  2️⃣ Identify the variable that is manipulated

  3️⃣ Identify the variable that is measured

  4️⃣ Determine which variable is the cause and which is the effect
• In a graph, the independent variable is positioned on the x-axis.
• The average rate of change measures the average change in y for each unit change in x.
• Match the term with its definition:

  Rate of change ↔️ How one variable changes in relation to another

  Δy ↔️ Change in the y-variable

  Δx ↔️ Change in the x-variable
• If a car travels 120 miles in 2 hours, its average speed is 60 miles per hour.


  True
• In a graph, the dependent variable is positioned on the y-axis.
• What is the independent variable in a relationship between two variables?

  The variable that is manipulated
• The independent variable is always positioned on the y-axis of a graph.

  False
• The dependent variable is measured or observed
• What does the average rate of change measure?

  Change in one variable per unit change in another
• x₂ and x₁ in the average rate of change formula represent the ending and starting x-values, respectively.

  True
• The instantaneous rate of change measures change at a specific point
• What does the rate of change formula measure?

  How one variable changes in relation to another