Topic 1: Attributes of Absolute Value

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 is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function intersects the y-axis, represented as (0, y).

Front

What is the domain of the absolute value function?

Back

The domain of the absolute value function is all real numbers, represented as (-∞, ∞).

Front

What is the range of the absolute value function?

Back

The range of the absolute value function is all non-negative real numbers, represented as [0, ∞).

Front

What is the axis of symmetry in a graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves. For the absolute value function, it is x = h, where h is the x-coordinate of the vertex.

Front

How do you find the y-intercept of an absolute value function?

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What is the vertex of an absolute value function?

Back

The vertex is the highest or lowest point of the graph, depending on the direction it opens. For the function y = a|x - h| + k, the vertex is (h, k).

Front

What does the parameter 'a' in the absolute value function affect?

Back

The parameter 'a' affects the vertical stretch or compression and the direction of the graph. If a > 0, the graph opens upwards; if a < 0, it opens downwards.

Front

What is the effect of changing the value of 'h' in the function y = a|x - h| + k?

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of changing the value of 'k' in the function y = a|x - h| + k?

Back

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