2.2 Graphs

• What feature of a reciprocal graph indicates its limits as x approaches certain values?

  Asymptotes
• Match the graph type with its use or example:

  Line Graph ↔️ Show changes in data over time

  Bar Graph ↔️ Compare discrete categories

  Pie Chart ↔️ Show proportions of a whole

  Scatter Plot ↔️ Identify correlations
• Match the axis with its definition:

  x-axis ↔️ Horizontal axis, independent variable

  y-axis ↔️ Vertical axis, dependent variable
• The x-axis represents the variable that is controlled or manipulated.


  True
• Match the graph type with its equation and shape:

  Linear Graph ↔️ $y =$$mx +$$b$, Straight line

  Quadratic Graph ↔️ $y =$$ax^{2} +$$bx +$$c$, Parabola

  Cubic Graph ↔️ $y =$$ax^{3} +$$bx^{2} +$$cx +$$d$, S-shaped curve

  Reciprocal Graph ↔️ $y =$$\frac{k}{x}$, Hyperbola
• What type of graph is described by the equation \( y = ax^2 + bx + c \)?

  Parabola
• The equation of a graph determines its shape.


  True
• Graphs can be used to visually represent relationships between variables.


  True
• Linear graphs have a constant rate of change, while quadratic graphs have a variable rate of change.


  True
• What is the primary purpose of graphs?

  Interpret and analyze data
• Steps to plot points on a graph using coordinates:

  1️⃣ Identify the coordinates (x, y)

  2️⃣ Locate the x-coordinate on the x-axis

  3️⃣ Locate the y-coordinate on the y-axis

  4️⃣ Plot the point at the intersection
• The vertical line from 2 and the horizontal line from 3 intersect at the point (2, 3)
• A linear graph has the equation y = mx + b
• The constants in the quadratic equation y = ax^2 + bx + c determine the shape and position
• In the equation y = 2x + 3, the y-intercept is located at the point (0, 3)
• What is the general form of a quadratic equation?

  $y =$$ax^{2} +$$bx +$$c$
• What are the key features of a graph that provide important insights?

  Shape and key features
• What does the y-intercept in a linear graph represent?

  Starting value of dependent variable
• Asymptotes in a reciprocal graph are vertical or horizontal lines that the graph approaches but never touches.


  True
• What does the x-axis represent in a coordinate system?

  Independent variable
• To plot a point, place a dot at the intersection of the vertical line from the x-coordinate and the horizontal line from the y-coordinate
• What are the axes used in a coordinate graph?

  x-axis and y-axis
• The point (0, 0) is located at the origin of the graph.


  True
• Match the graph type with its equation:

  Linear Graph ↔️ $y =$$mx +$$b$

  Quadratic Graph ↔️ $y =$$ax^{2} +$$bx +$$c$
• The y-intercept is the point where the graph crosses the y-axis
• What is the general form of a quadratic equation?

  $y =$$ax^{2} +$$bx +$$c$
• What is the general form of a linear equation?

  $y =$$mx +$$b$
• What is the first step in drawing a graph from an equation?

  Identify the equation type
• What two features should you identify in a linear graph?

  Slope and y-intercept
• What does the turning point of a quadratic graph represent?

  Maximum or minimum value
• What type of numbers should you use for graph scales to ensure ease of interpretation?

  Round numbers
• Quadratic graphs have x-intercepts where y equals zero

  True
• A graph is a visual representation of the relationship between two or more variables
• Graphs can reveal patterns and trends in data more effectively than raw numbers alone.


  True
• Understanding the role of the x-axis and y-axis is crucial for interpreting graphs.


  True
• Steps to plot points on a graph:

  1️⃣ Identify the coordinates

  2️⃣ Locate the x-coordinate on the x-axis

  3️⃣ Locate the y-coordinate on the y-axis

  4️⃣ Plot the point at the intersection
• The equation of a graph determines its shape.


  True
• A cubic graph has the equation \( y = ax^3 + bx^2 + cx + d \) and its shape is an S-shaped
• A linear graph has the equation \( y = mx + b \) and its shape is a straight line.
• What is the relationship represented by a linear graph?

  Linear relationship