Transformations of Absolute Value Functions Review

Front

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

Back

The vertex is the point (h, k).

Front

What does the 'a' in the function f(x) = a|x - h| + k represent?

Back

The 'a' represents the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

How does a positive 'a' value affect the graph of an absolute value function?

Back

It opens upwards and is stretched vertically if |a| > 1 or compressed if |a| < 1.

Front

How does a negative 'a' value affect the graph of an absolute value function?

Back

It opens downwards and is stretched vertically if |a| > 1 or compressed if |a| < 1.

Front

What is the effect of the term 'h' in the function f(x) = a|x - h| + k?

Back

The term 'h' represents a horizontal shift; the graph shifts right if h > 0 and left if h < 0.

Front

What is the effect of the term 'k' in the function f(x) = a|x - h| + k?

Back

The term 'k' represents a vertical shift; the graph shifts up if k > 0 and down if k < 0.

Front

What is the vertex of the function f(x) = 4|x + 2| - 3?

Back

The vertex is (-2, -3).

Front

What is the vertex of the function f(x) = 2|x - 4|?

Back

The vertex is (4, 0).

Front

Write the absolute value function for a reflection across the x-axis and a vertical shift down 3 units from f(x) = |x|.

Back

f(x) = -|x| - 3.

Front

What is the vertex of the function f(x) = -2|x + 3| - 2?

Back

The vertex is (-3, -2).