Translating Absolute Value Graphs: Domain and Range Insights

What is the basic shape of the graph of an absolute value function?

• A straight line

• A circle

• A parabola

• A V-shape

How does the graph of y = |x| change when it is translated 3 units up?

• It shifts 3 units up

• It shifts 3 units to the right

• It shifts 3 units down

• It shifts 3 units to the left

What happens to the graph of y = |x| when it is translated 2 units to the left?

• It shifts 2 units up

• It shifts 2 units to the left

• It shifts 2 units to the right

• It shifts 2 units down

What is the domain of the function y = |x|?

• All negative numbers

• All integers

• All positive numbers

• All real numbers

If the graph of y = |x| is translated 4 units down, what is the new range?

• y ≤ 4

• y ≥ 4

• y ≤ -4

• y ≥ -4

How do you solve the equation |x + 3| = 5?

• x = 2 or x = -8

• x = 8 or x = -2

• x = 2 or x = -2

• x = 5 or x = -5

What is the effect of a negative sign inside the absolute value function, such as y = |x - 2|?

• The graph shifts 2 units up

• The graph shifts 2 units to the left

• The graph shifts 2 units to the right

• The graph shifts 2 units down

If the equation is y = |x + 5|, where is the vertex of the graph located?

• (-5, 0)

• (0, 5)

• (5, 0)

• (0, -5)

What is the range of the function y = |x| + 3?

• y ≥ 3

• y ≤ -3

• y ≤ 3

• y ≥ -3

How do you write the equation for an absolute value function shifted 7 units to the left?

• y = |x| - 7

• y = |x| + 7

• y = |x + 7|

• y = |x - 7|