Absolute Value

Front

What is the equation of the absolute value function?

Back

f(x) = |x| + k, where k is a vertical shift.

Front

What does the transformation 'right 3, up 2' indicate for the function f(x) = |x|?

Back

The function is shifted 3 units to the right and 2 units up, resulting in f(x) = |x - 3| + 2.

Front

How does the graph of y = |x| + 6 differ from the basic absolute value graph?

Back

The graph is shifted up 6 units.

Front

What is the vertex of the function y = 4|x| + 1?

Back

The vertex is at the point (0, 1).

Front

How has the graph of y = |x + 8| + 3 been transformed from the basic graph?

Back

The graph is shifted left 8 units and up 3 units.

Front

What is the general form of an absolute value function?

Back

f(x) = a|bx - h| + k, where (h, k) is the vertex.

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 (upward if a > 0, downward if a < 0).

Front

What is the effect of changing 'k' in the function f(x) = |x| + k?

Back

Changing 'k' results in a vertical shift of the graph; if k is positive, the graph shifts up, and if k is negative, it shifts down.

Front

How do you determine the vertex of the function y = a|x - h| + k?

Back

The vertex is located at the point (h, k).

Front

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

Back

The absolute value ensures that the output is always non-negative, reflecting the distance from zero.