Absolute Value Attributes

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 do you graph the function f(x) = |x - 5|?

Back

The graph of f(x) = |x - 5| is a V-shaped graph that opens upwards, with the vertex at the point (5, 0).

Front

What is the vertex of the function y = 2|x - 5| + 6?

Back

The vertex of the function y = 2|x - 5| + 6 is at the point (5, 6).

Front

What is the axis of symmetry for the function f(x) = |x - 5|?

Back

The axis of symmetry for the function f(x) = |x - 5| is the vertical line x = 5.

Front

What does the term 'line of symmetry' refer to in absolute value functions?

Back

The line of symmetry is a vertical line that divides the graph into two mirror-image halves. For f(x) = |x - h|, the line of symmetry is x = h.

Front

What is the y-intercept of the function f(x) = |x - 5|?

Back

The y-intercept of the function f(x) = |x - 5| is at the point (0, 5).

Front

How do you find the x-intercepts of the function f(x) = |x - 5|?

Back

To find the x-intercepts, set f(x) = 0. For f(x) = |x - 5|, the x-intercept is at x = 5.

Front

What is the range of the function f(x) = |x - 5|?

Back

The range of the function f(x) = |x - 5| is [0, ∞) because the absolute value is always non-negative.

Front

What is the effect of multiplying an absolute value function by a positive constant?

Back

Multiplying an absolute value function by a positive constant stretches the graph vertically. For example, y = 2|x - 5| is stretched compared to y = |x - 5|.

Front

What happens to the graph of an absolute value function when a constant is added outside the absolute value?

Back

Adding a constant outside the absolute value shifts the graph vertically. For example, y = |x - 5| + 6 shifts the graph up by 6 units.