# 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.