LT # 3 Absolute Value

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where a, b, c, and d are constants.

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 does the parameter 'b' in the absolute value function affect?

Back

The parameter 'b' affects the horizontal stretch or compression of the graph.

Front

What does the parameter 'c' in the absolute value function represent?

Back

The parameter 'c' represents a horizontal shift of the graph. If c is positive, the graph shifts left; if negative, it shifts right.

Front

What does the parameter 'd' in the absolute value function represent?

Back

The parameter 'd' represents a vertical shift of the graph. If d is positive, the graph shifts up; if negative, it shifts down.

Front

What is the vertex of an absolute value function?

Back

The vertex is the point where the graph changes direction, typically represented as (h, k) in the function f(x) = a|bx + c| + d.

Front

How do you find the vertex of the function f(x) = -|2x + 6| + 5?

Back

To find the vertex, set the inside of the absolute value to zero: 2x + 6 = 0, which gives x = -3. Then, substitute x back into the function to find y: f(-3) = -|0| + 5 = 5. So, the vertex is (-3, 5).

Front

What is the shape of the graph of an absolute value function?

Back

The graph of an absolute value function is a 'V' shape.

Front

What transformation occurs when the function is f(x) = -|x|?

Back

The graph reflects over the x-axis.