Sketching Modulus Graphs
What is a modulus function?
- The modulus function makes any ‘input’ positive
- This is sometimes called the absolute value (of the input)
- The modulus function is indicated by a pair of vertical lines being written around the input
- Similar to how brackets are used
- e.g.
What types of modulus graphs will I need to sketch?
- Modulus graphs required will be of linear, or quadratic form
- Linear form will be
- Quadratic form will be
- Often, there will be two graphs to sketch as this helps with solving equations involving modulus functions
- In linear form, equations could be of the form
- One side of the equation may not involve the modulus
- One side may have a constant term only (i.e. and/or
- In quadratic form, equations could be of the form
- In linear form, equations could be of the form
- In both cases, graphs of the left hand side and right hand side drawn on the same diagram will reveal the number of intersections of the graphs (and so the number of solutions to the equation)
How do I sketch the graph of the modulus of a function: y = |f(x)|?
STEP 1
Pencil in the graph of y = f(x)
STEP 2
Reflect anything below the x-axis, in the x-axis, to get y = |f(x)|
- Note in particular that the -axis intercept, if negative on the graph of will be positive on the graph of
- At the -axis intercepts, the graph will have a sharp -shape
- this is not a smooth curve like with a turning point
- if the graph is of the form then the graph would be wholly negative and the -axis intercepts would have a sharp -shape