Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What does the graph of the absolute value function look like?

Back

The graph of the absolute value function is a V-shaped graph that opens upwards.

Front

What transformation does the equation y = -|x| represent?

Back

The equation y = -|x| represents a reflection of the absolute value function across the x-axis.

Front

What does the equation y = |x| + 4 represent in terms of transformation?

Back

The equation y = |x| + 4 represents a vertical shift of the absolute value function upwards by 4 units.

Front

How does the equation y = |x - 3| transform the parent function?

Back

The equation y = |x - 3| represents a horizontal shift of the absolute value function to the right by 3 units.

Front

What is the effect of the negative sign in front of the absolute value, as in y = -|x + 2|?

Back

The negative sign reflects the graph of the absolute value function across the x-axis.

Front

If the equation is y = |x| - 5, what transformation occurs?

Back

The equation y = |x| - 5 represents a vertical shift of the absolute value function downwards by 5 units.

Front

What does the equation y = |x + 1| - 2 indicate about the transformations?

Back

The equation y = |x + 1| - 2 indicates a horizontal shift to the left by 1 unit and a vertical shift downwards by 2 units.

Front

What is the general form of an absolute value function?

Back

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