Absolute Value

Front

What is the equation of the absolute value function?

Back

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

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D