Absolute Value Graphs

Front

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

Back

The graph of y = |x| is shifted down 7 units.

Front

What is the parent function of absolute value graphs?

Back

The parent function is f(x) = |x|.

Front

How does the graph of g(x) = |x - 2| differ from the parent function?

Back

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

Front

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

Back

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

Front

What is the general form of an absolute value function?

Back

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

Front

How do you determine the vertex of the function f(x) = |x - 2| + 4?

Back

The vertex is at the point (2, 4).

Front

What effect does the coefficient 'a' have in the function f(x) = a|x|?

Back

The coefficient '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 maximum value of the function f(x) = -|x| + 4?

Back

The maximum value is 4, occurring at the vertex (0, 4).

Front

How do you find the x-intercepts of the function f(x) = |x - 3|?

Back

Set f(x) = 0 and solve for x: |x - 3| = 0, which gives x = 3.

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, creating a V-shaped graph.