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

How does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What effect does the equation y = |x - h| have on the graph?

Back

The graph of y = |x - h| shifts the graph of y = |x| to the right by h units if h > 0, and to the left by h units if h < 0.

Front

What effect does the equation y = |x| + k have on the graph?

Back

The graph of y = |x| + k shifts the graph of y = |x| up by k units if k > 0, and down by k units if k < 0.

Front

What is the transformation of the graph for y = |x| - 3?

Back

The graph of y = |x| - 3 is shifted down by 3 units.

Front

What is the transformation of the graph for y = |x + 4|?

Back

The graph of y = |x + 4| is shifted left by 4 units.

Front

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

Back

The vertex of the graph y = |x - 5| + 2 is at the point (5, 2).

Front

What is the transformation of the graph for y = |x| + 1?

Back

The graph of y = |x| + 1 is shifted up by 1 unit.

Front

What does the negative sign in y = -|x| indicate about the graph?

Back

The negative sign indicates that the graph opens downwards, creating an upside-down V shape.

Front

How does the graph of y = |x - 2| + 3 differ from y = |x|?

Back

The graph of y = |x - 2| + 3 is shifted right by 2 units and up by 3 units compared to y = |x|.