# 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.