Graphing Absolute Value Functions and Their Shifts

What is the basic form of an absolute value function?

• f(x) = x + 2

• f(x) = 2x

• f(x) = |x|

• f(x) = x^2

What is the vertex of the basic absolute value function f(x) = |x|?

• (2, 2)

• (0, 0)

• (1, 1)

• (-1, -1)

How do you determine the vertex of the function g(x) = |x - 2| + 3?

• By looking at the coefficients of x

• By identifying the values subtracted from x and added outside the absolute value

• By setting x to zero

• By finding the slope

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

• (3, 2)

• (-2, -3)

• (2, 3)

• (0, 0)

How does the graph of g(x) = |x - 2| + 3 shift compared to the basic absolute value function?

• Right 2 units and up 3 units

• Left 2 units and up 3 units

• Left 2 units and down 3 units

• Right 2 units and down 3 units

What is the vertex of the function h(x) = |x + 4| - 1?

• (4, 1)

• (-4, -1)

• (-4, 1)

• (4, -1)

How does the graph of h(x) = |x + 4| - 1 shift compared to the basic absolute value function?

• Right 4 units and down 1 unit

• Left 4 units and down 1 unit

• Right 4 units and up 1 unit

• Left 4 units and up 1 unit

What happens to the graph of an absolute value function when you add a value inside the absolute value bars?

• It shifts down

• It shifts to the left

• It shifts to the right

• It shifts up

What happens to the graph of an absolute value function when you subtract a value outside the absolute value bars?

• It shifts down

• It shifts to the right

• It shifts up

• It shifts to the left

What is the effect of adding a value outside the absolute value bars on the graph?

• It shifts to the left

• It shifts to the right

• It shifts down

• It shifts up