Absolute Value Transformations and Equations

Front

What is the definition of absolute value?

Back

The distance of a number from zero on the number line.

Front

Solve the equation: |x - 5| = 3

Back

x = 2 and x = 8.

Front

What does the equation |a| = b imply about 'a'?

Back

It implies that a = b or a = -b.

Front

Describe the transformation: |x| + 3

Back

This represents a vertical shift of the absolute value function upwards by 3 units.

Front

Solve the equation: |3x + 1| = 7

Back

x = 2 and x = -rac{8}{3}.

Front

What is the effect of a negative sign in front of an absolute value?

Back

It reflects the graph of the absolute value function across the x-axis.

Front

Solve the equation: |2x - 4| = 0

Back

x = 2.

Front

What is the graphical representation of |x|?

Back

A V-shaped graph that opens upwards with the vertex at the origin.

Front

Solve the equation: |x + 3| = 5

Back

x = 2 and x = -8.

Front

What is the transformation of the function |x| when it is written as |x - 4|?

Back

It shifts the graph of |x| to the right by 4 units.