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 - h| + k transform the basic graph of y = |x|?

Back

The graph shifts horizontally by h units and vertically by k units. If h is positive, it shifts right; if negative, left. If k is positive, it shifts up; if negative, down.

Front

What is the vertex of the graph y = |x - 3| + 2?

Back

The vertex is at the point (3, 2).

Front

What effect does a negative sign in front of the absolute value have on the graph?

Back

A negative sign reflects the graph across the x-axis, turning it upside down.

Front

What is the range of the function y = |x|?

Back

The range is y ≥ 0, as absolute values cannot be negative.

Front

How do you find the x-intercepts of the graph y = |x - 2|?

Back

Set y = 0: |x - 2| = 0, which gives x = 2. The x-intercept is (2, 0).

Front

What is the equation of the graph that has a vertex at (0, -3) and opens upwards?

Back

The equation is y = |x| - 3.

Front

What is the effect of adding a constant outside the absolute value, like in y = |x| + 4?

Back

It shifts the graph vertically upwards by 4 units.

Front

What is the equation of the graph that has a vertex at (-2, 5) and opens downwards?

Back

The equation is y = -|x + 2| + 5.