Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Absolute values - graphs.
Test Yourself 1.


 

Graph each of equations 1 - 8 and describe the transformations from the basic graph of y = |x|.
Graphing equalities. 1. y = |3x| 2. y = |x - 1|
  3. y = |2 - x| 4. y = 2 + |x|
  5. y = |x + 1| - 1 6. y = |0.5x + 4| - 2
  7. y = 3 - |2x| 8. y = 4 - |3x - 9|
Solving equations graphically. 9. By sketching an appropriate graph, show how many solutions there are when the equations

y = |x - 3| and y = 2

are solved simultaneously.

 10. By sketching an appropriate graph, show how many solutions there are when the equations

y = |x + 1| + 2 and y = 2

are solved simultaneously.
  11. By sketching an appropriate graph, show how many solutions there are when the equations

y = |2x - 1| + 1 and 2y -1 = 0

are solved simultaneously.

 12. By sketching an appropriate graph, show how many solutions there are when the equations

y = 1 - |x + 1| and y = 1

are solved simultaneously.
  13. By sketching an appropriate graph, show how many solutions there are when the equations

y = |x + 1| + 2 and x - y = 1

are solved simultaneously.

 14. By sketching an appropriate graph, show how many solutions there are when the equations

y = 3 - |3x - 2| and
y = 2 - 3x

are solved simultaneously.