# Drawing and Sketching of Functions

## Drawing and Sketching of Functions

# General Concepts

- The process of
**drawing and sketching functions**is a key component of graphical algebra. - This concept involves representing mathematical functions visually using a set of axes.

# Functions and Graphs

**Linear functions**have a constant rate of change and their graphs are straight lines.**Quadratic functions**have a variable squared as their highest power. Their graphs typically form a parabola.**Cubic functions**contain a variable raised to the power of three. Their graphs can take on a variety of shapes with turning points.**Exponential functions**rise or decay rapidly and their graphs vary accordingly.**Trigonometric functions**such as sine, cosine and tangent produce regular, oscillating graphs.

# Key Steps in Drawing

- Determine the
**type of function**you are dealing with. Understanding the form of the function will guide how you sketch its graph. - Identify and plot any
**intercepts with axes**. These are points where your function crosses the x or y axis. - For quadratic functions, find the
**vertex of the parabola**(the turning point) and plot this. - Consider the
**end behavior of the function**as x tends to positive or negative infinity to determine the general direction of the graph. - Sketch the curve using the plotted points as a guide. Include any important features of the function.

# Important Reminders

- Always consider the
**domain and range**of the function. These will provide boundaries within which to sketch your graph. - Where necessary, use a
**table of values**to find exact points on the graph.

# Conclusion

- Mastering the
**sketching of functions**is immensely useful within further mathematics. It can help make abstract concepts more concrete, and can simplify the understanding of more complex mathematical relationships.