Graphing Absolute Value Functions: Domain and Range Insights

What shape does the graph of the parent function of the absolute value of x resemble?

• A U shape

• A V shape

• A straight line

• A parabola

What happens to the graph of the absolute value function if a negative sign is placed outside?

• It shifts to the right

• It opens downward

• It shifts to the left

• It opens upward

What effect does a negative sign inside the absolute value function have on its graph?

• It reflects the graph over the x-axis

• No effect

• It reflects the graph over the y-axis

• It shifts the graph downwards

For the function y = -|x|, where does the graph open?

• Downwards

• Upwards

• To the left

• To the right

What is the domain of an absolute value function without modifications?

• -1 to 1

• Negative infinity to infinity

• Negative infinity to 0

• 0 to infinity

How does a graph of an absolute value function change with a vertical shift upwards?

• The slope increases

• The graph becomes narrower

• The vertex moves up

• The graph opens downward

If the absolute value function has a slope of 2, how does the graph change compared to the parent function?

• It becomes steeper

• It shifts to the right

• It becomes wider

• It shifts to the left

What does a horizontal shift in the graph of an absolute value function represent?

• Change in slope

• Change in vertex position horizontally

• Change in range

• Change in domain

What is the range of the function y = |x| + 2?

• -infinity to 2

• 2 to infinity

• -2 to infinity

• 0 to infinity

What is the range of a graph that opens downward with its vertex at (0, -3)?

• -3 to 0

• -infinity to -3

• 0 to infinity

• -3 to infinity