Interpretation of Graphs

Interpretation of Graphs

Understanding Graphs

  • A graph visually represents data to help interpret complex data easily.
  • The x-axis (horizontal) and y-axis (vertical) contain numerical values related to the data being shown.

Plotting Points

  • Every point on a graph corresponds to an ordered pair (x, y), with x being the value on the x-axis and y being the value on the y-axis.
  • The point (0, 0) is known as the origin.

Types of Graphs

  • Line graph: A linear function is represented as a straight line on a graph.
  • Parabolic graph: Quadratic functions are represented as curves, either opening upwards or downwards.
  • Exponential graph: Represents exponential growth or decay.

Understanding Line Graph Properties

  • The gradient (or slope) of a line graph gives the rate of change.
  • A line that goes up from left to right has a positive gradient.
  • A line that goes down from left to right has a negative gradient.

Understanding Curve Graph Properties

  • The highest or lowest point of a parabolic graph is known as the vertex.
  • x-intercepts are where the graph crosses the x-axis, and they are also the roots of the function.

Interpreting Graphs

  • The graph of a function shows all the points (x, y) that satisfy the equation.
  • The y-intercept is where the graph crosses the y-axis (where x = 0).
  • The x-intercept(s) is/are where the graph crosses the x-axis (where y = 0).
  • Symmetry about the y-axis means the left and right sides of the graph mirror each other.
  • Asymptotes are lines that the graph approaches but never touches.

Graph Transformations

  • Translations: A graph’s position is moved up, down, left, or right without changing its shape.
  • Reflections: The graph is flipped over an axis.
  • Dilation: The graph is stretched or shrunk vertically or horizontally.

Remember to always check the scale of the graph axis labels for proper interpretation of the graph.