Absolute Value Transformations

Front

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

Back

The vertex is the point (h, k).

Front

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

Back

The value of 'a' affects the vertical stretch or compression and the direction of the opening. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What does the transformation 'right 4' mean in the context of the function y = |x|?

Back

It means the graph of the function is shifted 4 units to the right along the x-axis.

Front

What is the parent function of absolute value transformations?

Back

The parent function is y = |x|.

Front

If the function is y = |x + 2|, what transformation has occurred compared to the parent function?

Back

The graph has shifted 2 units to the left.

Front

What is the effect of adding a constant 'k' to the absolute value function y = |x|?

Back

Adding a constant 'k' shifts the graph vertically by 'k' units. If 'k' is positive, it shifts up; if negative, it shifts down.

Front

For the function y = -4|x + 2| + 5, what is the vertex?

Back

The vertex is (-2, 5).

Front

What does the transformation 'up 2' indicate for the function y = |x|?

Back

It indicates that the graph of the function is shifted 2 units upwards along the y-axis.

Front

How do you determine the vertex of the function y = 2|x - 3| + 1?

Back

The vertex can be found at the point (3, 1), where h = 3 and k = 1.

Front

What is the significance of the vertex in an absolute value function?

Back

The vertex represents the minimum or maximum point of the graph, depending on the value of 'a'.