Absolute Value Graph Transformations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the equation y = |x| represent?

Back

It represents a V-shaped graph that opens upwards with its vertex at the origin (0,0).

Front

How does the graph of y = |x - h| shift?

Back

The graph shifts horizontally to the right by h units if h is positive and to the left by h units if h is negative.

Front

How does the graph of y = |x| + k shift?

Back

The graph shifts vertically upwards by k units if k is positive and downwards by k units if k is negative.

Front

What effect does a negative sign have in the equation y = -|x|?

Back

It reflects the graph of y = |x| across the x-axis, creating an upside-down V shape.

Front

What is the vertex of the graph y = |x - 3| + 4?

Back

The vertex is at the point (3, 4).

Front

How do you identify the vertex of the graph y = |x + 2| - 5?

Back

The vertex is at the point (-2, -5).

Front

What transformation does y = |x| - 2 represent?

Back

It represents a downward shift of the graph by 2 units.

Front

What is the effect of the equation y = |x + 4| + 3 on the graph?

Back

It shifts the graph left by 4 units and up by 3 units.

Front

How do you determine the direction of the opening of the graph y = a|x|?

Back

If a > 0, the graph opens upwards; if a < 0, it opens downwards.