Absolute Value Functions

Front

What does the equation y = |x| - 7 represent in terms of graph transformation?

Back

The graph of y = |x| slides down 7 units.

Front

What is the vertex of the absolute value function f(x) = |x|?

Back

The vertex of the function f(x) = |x| is at the point (0, 0).

Front

How does the equation y = |x - 3| affect the graph of the parent function f(x) = |x|?

Back

The graph of y = |x - 3| slides to the right by 3 units.

Front

What is the effect of adding a constant outside the absolute value function, such as in f(x) = |x| + 3?

Back

The graph slides up 3 units.

Front

What is the effect of adding a constant inside the absolute value function, such as in f(x) = |x + 4|?

Back

The graph slides to the left by 4 units.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where (h, k) is the vertex.

Front

What does the parameter 'a' in the absolute value function f(x) = a|x| indicate?

Back

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

Front

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

Back

The vertex is at the point (-4, 3).

Front

How does the graph of g(x) = |x - 2| compare to the parent function f(x) = |x|?

Back

The graph of g(x) = |x - 2| is shifted to the right by 2 units.

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 direction of the opening.