Sketching Graphs

Understanding Sketching Graphs

  • Sketching graphs involves drawing a rough estimation of a graph given a mathematical function.
  • It includes understanding the shape, intercepts (x and y) and any key points or regions.
  • Plotting can help give a more detailed picture of the graph.

Sketching Straight Line Graphs

  • For straight line graphs, find the y-intercept and the gradient first.
  • The general straight line equation is y = mx + c, where m is the gradient and c is the y-intercept.
  • Plot the intercept first on the y-axis and then use the gradient to find another point.

Sketching Quadratic Graphs

  • The graph of a Quadratic function, or a Parabola, is a smooth curve.
  • The equation is in the form y = ax^2 + bx + c, where the value of a determines whether the parabola opens upwards (a > 0) or downwards (a < 0).
  • The vertex and x/y-intercepts should be found and marked.

Sketching Cubic Graphs

  • Cubic graphs are derived from cubic functions of the form y = ax^3 + bx^2 + cx + d.
  • Identify key features such as the point of inflection.

Sketching Exponential and Logarithmic Graphs

  • The shape of exponential graphs (y = a^x) usually rise or fall very steeply and may approach, but never meets, the x-axis.
  • Logarithmic graphs (y = logax) are the inverse of exponential graphs and have a vertical asymptote.
  • Identify the asymptotes (the line that the graph approaches but never reaches).

Remember to label the axes and plots in your sketches.