Absolute Value Graphs

Front

What is the general form of an absolute value function?

Back

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

Front

What does the 'h' in the absolute value function f(x) = |x - h| + k represent?

Back

The horizontal shift of the graph; it moves the graph left or right.

Front

What does the 'k' in the absolute value function f(x) = |x - h| + k represent?

Back

The vertical shift of the graph; it moves the graph up or down.

Front

How does the graph of f(x) = |x| change when you add a constant to it, such as in f(x) = |x| + 4?

Back

The graph shifts vertically upwards by 4 units.

Front

How does the graph of f(x) = |x| change when you subtract a constant from it, such as in f(x) = |x| - 7?

Back

The graph shifts vertically downwards by 7 units.

Front

What effect does the transformation g(x) = |x - 2| have on the graph of f(x) = |x|?

Back

The graph shifts horizontally to the right by 2 units.

Front

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

Back

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

Front

What is the parent function of absolute value graphs?

Back

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

Front

How do you determine the transformations applied to the parent function from the equation f(x) = |x - 3| + 2?

Back

The graph shifts right 3 units and up 2 units.

Front

What is the effect of a negative sign in front of the absolute value, such as in f(x) = -|x|?

Back

The graph reflects over the x-axis.