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?

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 equation y = |x - h| shifts the graph of y = |x| horizontally to the right by h units if h is positive, and to the left if h is negative.

Front

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

Back

The equation y = |x| + k shifts the graph of y = |x| vertically upwards by k units if k is positive, and downwards if k is negative.

Front

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

Back

The vertex of the graph y = |x - 4| is at the point (4, 0).

Front

How does the graph of y = |x + 3| - 4 differ from y = |x|?

Back

The graph of y = |x + 3| - 4 is shifted left 3 units and down 4 units from the graph of y = |x|.

Front

What is the transformation of the graph y = |x| - 2?

Back

The graph y = |x| - 2 is shifted down 2 units from the graph of y = |x|.

Front

How do you identify the direction of the shift in the equation y = |x - 9| + 1?

Back

The graph is shifted right 9 units and up 1 unit from the graph of y = |x|.

Front

What does the equation y = |x + 4| represent in terms of graph transformation?

Back

The equation y = |x + 4| shifts the graph of y = |x| left 4 units.

Front

What is the effect of a negative sign in front of the absolute value, such as in y = -|x|?

Back

The negative sign reflects the graph of y = |x| across the x-axis.