Absolute Value Transformations Practice

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 it mean to vertically compress a graph?

Back

A vertical compression occurs when the graph of a function is squeezed towards the x-axis, typically by a factor less than 1.

Front

How does shifting a graph to the right affect its equation?

Back

Shifting a graph to the right involves replacing x with (x - h) in the equation, where h is the number of units to shift.

Front

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

Back

The vertex is the point (h, k), which represents the minimum or maximum point of the graph.

Front

What transformation does the negative sign in front of an absolute value function indicate?

Back

The negative sign indicates a reflection over the x-axis.

Front

How do you identify the vertical stretch or compression factor in an absolute value function?

Back

The factor is determined by the coefficient 'a' in the function y = a|x - h| + k. If |a| > 1, it's a stretch; if |a| < 1, it's a compression.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. If positive, it shifts up; if negative, it shifts down.

Front

What does the transformation 'left 5' mean in terms of the function's equation?

Back

To shift a graph left by 5 units, replace x with (x + 5) in the function's equation.

Front

How do you determine the transformations from the parent graph to a transformed graph?

Back

Identify changes in the equation such as shifts, stretches, compressions, and reflections to describe the transformations.

Front

What is the general form of an absolute value function?

Back

The general form is y = a|x - h| + k, where (h, k) is the vertex.