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

Algebra - Absolute values - graphs.
Test Yourself 1 - Solutions.


 

Graph each of equations 1 - 8 and describe the transformations from the basic graph
of y = |x|.
Graphing equalities. 1.

The graph is not moved horizontally or vertically. The gradient is increased to 3.

 2.

The graph is moved 1 unit to the right. The gradient is unchanged.
  3.

The graph is moved 2 units to the right. The gradient is unchanged.

 4.

The graph is moved 2 units upwards. The gradient is unchanged.
  5.

The graph is moved 1 unit to the left and down unit. The gradient is unchanged.

 6.

The graph is moved 8 units to the left and down 2 units. The gradient is reduced by one half to m = 0.5.
  7.

The graph is moved 3 units and inverted by the negative sign. The gradient has doubled to 2.

 8.

The graph is moved 4 units up and 3 units to the right. The gradient is steeped having been increased by a factor of 3.
Solving equations graphically. 9.

There are two solutions - at (1, 2) and at (5, 2).

 10.

There is only one solution - at (-1, 2).
  11.

There are no solutions - the lines do not intersect.

 12.

There is only solution - at (-1, 1) - where the given line intersect at the vertex of the absolute value graph.
  13.

There are no solutions - the lines do not intersect as the vertex of the absolute value graph is above the line and the right section is parallel to the line.

 14. There is only solution - at (1/6, 0.5) - where the left section intersects the line. The right section is parallel to the line.