Absolute Value Graphing

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 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

How does the graph of y = |x - h| transform the parent function y = |x|?

Back

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

Front

What does the coefficient in front of the absolute value function indicate?

Back

The coefficient affects the width of the graph. A coefficient greater than 1 makes the graph narrower, while a coefficient between 0 and 1 makes it wider.

Front

What is the axis of symmetry for the graph of y = |x - h|?

Back

The axis of symmetry is the vertical line x = h.

Front

How do you determine the vertex of the graph y = a|x - h| + k?

Back

The vertex is located at the point (h, k).

Front

What transformation does y = |x| + k represent?

Back

The graph of y = |x| + k shifts the graph of y = |x| up by k units.

Front

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

Back

The graph of y = |x| - k shifts the graph of y = |x| down by k units.

Front

If the equation is y = -|x|, what does this indicate about the graph?

Back

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

Front

What is the effect of a negative coefficient in front of the absolute value function?

Back

A negative coefficient reflects the graph across the x-axis.