1.1 Describing how quantities change with respect to each other

• On which axis is the independent variable typically plotted?

  x-axis
• What does the y-axis represent on a graph?

  Dependent variable
• The graph of a quadratic functional relationship is a parabolic curve.


  True
• Steps to define a functional relationship

  1️⃣ Identify two quantities

  2️⃣ Determine if one depends on the other

  3️⃣ Describe the dependency with a function

  4️⃣ Verify that each input has one output
• What is the notation for the independent variable?

  `x`
• The shape and characteristics of the graph provide insights into the nature of the functional relationship.
• What does the shape of a graph indicate about a functional relationship?

  Its nature
• What type of curve represents an exponential functional relationship?

  Curved line
• The rate of change is calculated as the change in the dependent variable divided by the change in the independent variable.
• What is the rate of change for the function y = 2x + 3</latex>?

  2
• In a functional relationship, each input value of the independent variable corresponds to one output value of the dependent variable.
• The independent variable is what you change, and the dependent variable is what you measure.
• If \( y = f(x) = 2x + 3 \), the graph is a straight line with points like \((0, 3)\), \((1, 5)\), and (2, 7).
• In an exponential relationship, the dependent variable grows or decays proportionally to its current value.
• The dependent variable represents the input to the function.

  False
• An example of the independent variable is the number of hours studied, while the dependent variable is the exam score.
• What type of graph shows a constant change in the dependent variable for a given change in the independent variable?

  Straight line
• A linear functional relationship is represented by a straight line with a constant rate of change.

  True
• An inverse functional relationship is represented by a hyperbolic curve.

  True
• What does the slope of a line represent graphically?

  Rate of change
• The slope of a quadratic functional relationship changes as the independent variable changes.
• A positive slope indicates that the line rises from left to right.


  True
• An undefined slope is represented by a vertical line.


  True
• The slope indicates how quickly the dependent variable changes in relation to changes in the independent variable
• How is the slope of a line calculated?

  (change in y) / (change in x)
• What is the independent variable typically plotted on?

  x-axis
• The independent variable is typically plotted on the x-axis
• Match the functional relationship with its graphical representation:

  Linear ↔️ A straight line

  Quadratic ↔️ A parabolic curve

  Exponential ↔️ A curved line

  Inverse ↔️ A hyperbolic curve
• The rate of change for a linear relationship is constant.


  True
• The formula for the rate of change is (change in y) / (change in x)
• The slope of a line measures its steepness and direction on a graph.


  True
• A negative slope indicates that the function is decreasing
• The graphical representation of the instantaneous rate of change is the slope of a tangent
• The independent variable represents the input
• The output of a function is typically plotted on the y-axis.


  True
• The independent variable represents the input to a function.


  True
• Why is it crucial to understand the difference between independent and dependent variables?

  Analyzing functional relationships
• Functional relationships are often represented graphically using a coordinate plane.plane
• What type of curve represents a quadratic functional relationship?

  Parabolic curve
• What is a functional relationship between two quantities?

  Dependency between variables