Exploring Absolute Value Functions in Vertex Form

What is the standard form of an absolute value function?

• f(x) = ax^2 + bx + c

• f(x) = a|x - h| + k

• f(x) = ax + b

• f(x) = a(x - h)^2 + k

How does the graph of g(x) = |x| + 3 compare to the graph of f(x) = |x|?

• It is shifted 3 units to the right.

• It is shifted 3 units to the left.

• It is shifted 3 units up.

• It is shifted 3 units down.

What is the domain of the function g(x) = |x| + 3?

• x ≥ 0

• x ≠ 0

• x ≤ 0

• All real numbers

What is the range of the function m(x) = |x - 2|?

• y ≠ 0

• All real numbers

• y ≤ 0

• y ≥ 0

How does the graph of q(x) = 2|x| compare to the graph of f(x) = |x|?

• It is shrunk vertically by a factor of 2.

• It is shifted 2 units up.

• It is stretched vertically by a factor of 2.

• It is shifted 2 units down.

What transformation occurs when the function is p(x) = -1/2|x|?

• Vertical stretch by a factor of 2 and reflection over the x-axis.

• Vertical shrink by a factor of 1/2 and reflection over the x-axis.

• Vertical stretch by a factor of 1/2 and reflection over the y-axis.

• Vertical shrink by a factor of 2 and reflection over the y-axis.

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

• (-2, 3)

• (2, 3)

• (2, -3)

• (-2, -3)

How does the graph of g(x) = |1/2x - 1| compare to f(x) = |x|?

• It is stretched horizontally by a factor of 2.

• It is shifted 1 unit to the right.

• It is shrunk horizontally by a factor of 2.

• It is shifted 1 unit to the left.

What is the first transformation applied to g(x) = -2|x - 1| + 3?

• Vertical stretch by a factor of 2

• Reflection over the x-axis

• Shift 1 unit to the right

• Shift 3 units up

What is the final transformation applied to g(x) = -2|x - 1| + 3?

• Shift 3 units up

• Shift 1 unit to the right

• Reflection over the x-axis

• Vertical stretch by a factor of 2