Absolute value graphs

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 the vertex at the origin (0,0).

Front

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

Back

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

Front

What is the vertex of the function y = |x - h| + k?

Back

The vertex of the function y = |x - h| + k is the point (h, k).

Front

How does the value of 'h' in y = |x - h| + k affect the graph?

Back

The value of 'h' shifts the graph horizontally. If h is positive, the graph shifts right; if h is negative, it shifts left.

Front

How does the value of 'k' in y = |x - h| + k affect the graph?

Back

The value of 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What does a coefficient greater than 1 in y = a|x| indicate about the graph?

Back

A coefficient greater than 1 makes the graph narrower compared to the parent function y = |x|.

Front

What does a coefficient between 0 and 1 in y = a|x| indicate about the graph?

Back

A coefficient between 0 and 1 makes the graph wider compared to the parent function y = |x|.

Front

What is the effect of a negative coefficient in y = -a|x|?

Back

A negative coefficient reflects the graph across the x-axis, making it open downwards.

Front

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

Back

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