Exploring Two-Variable Absolute Value Equations

What is the definition of absolute value?

• The distance of a quantity from zero

• The sum of a quantity and zero

• The product of a quantity and zero

• The difference between a quantity and zero

What shape does the graph of y = |x| resemble?

• A circle

• A V-shape

• A parabola

• A straight line

What happens to the graph of y = |x| when you add a positive constant outside the absolute value?

• It shifts to the left

• It shifts to the right

• It shifts upward

• It shifts downward

How does subtracting a constant inside the absolute value affect the graph of y = |x|?

• It shifts the graph upward

• It shifts the graph downward

• It shifts the graph to the right

• It shifts the graph to the left

How does adding a constant inside the absolute value affect the graph of y = |x|?

• It shifts the graph to the left

• It shifts the graph to the right

• It shifts the graph upward

• It shifts the graph downward

What is the effect of multiplying the absolute value function by a positive constant greater than 1?

• It shifts the graph to the right

• It shifts the graph to the left

• It stretches the graph vertically

• It compresses the graph vertically

What does multiplying the absolute value function by a negative constant do to the graph?

• It shifts the graph downward

• It shifts the graph upward

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

What is the effect of a vertical compression on the graph of y = |x|?

• It shifts the graph to the left

• It makes the graph steeper

• It makes the graph flatter

• It shifts the graph to the right

In the equation y = a|x - h| + k, what does the parameter 'h' represent?

• Vertical stretch

• Horizontal shift

• Vertical shift

• Reflection

In the equation y = a|x - h| + k, what does the parameter 'k' represent?

• Reflection

• Horizontal shift

• Vertical stretch

• Vertical shift