Graphing Absolute Value Functions Flashcard Review

Front

What does the equation y = |x| - 7 do to the graph?

Back

It slides the graph down 7 units.

Front

What is the equation of the absolute value function that has a vertical stretch of 4 and a horizontal shift of 3 to the right?

Back

f(x) = 4|x - 3|

Front

Identify the function graphed by the equation f(x) = |x + 2| - 4.

Back

This function is shifted left 2 units and down 4 units from the parent function.

Front

How does the graph of y = \frac{1}{3}|x| + 3 compare in width to its parent function?

Back

The graph is wider than the parent function.

Front

What is the range of the function f(x) = |x| - 7?

Back

The range is [−7, ∞).

Front

What is the vertex of the function f(x) = 2|x + 1| - 3?

Back

The vertex is at the point (-1, -3).

Front

How does the coefficient of the absolute value affect the graph's steepness?

Back

A larger coefficient makes the graph steeper, while a smaller coefficient makes it wider.

Front

What transformation does the equation y = -|x| + 5 represent?

Back

It reflects the graph over the x-axis and shifts it up 5 units.

Front

What is the effect of adding a constant outside the absolute value function?

Back

It shifts the graph vertically.

Front

What is the effect of adding a constant inside the absolute value function?

Back

It shifts the graph horizontally.