Absolute Value Functions and Translations

What is the vertex of the graph of f(x) = |x + 5| - 6?

C (-5, -6)

Which graph represents the function f(x) = |x + 3|?

B

The graph of g(x) = |x - h| + k is shown on the coordinate grid. What must be true about the signs of h and k?

D h must be negative and k must be positive.

The graph of is shown. On which interval is this graph increasing?

NOT C (6, ∞)

Which graph represents the function r(x) = |x - 2| - 1

A

The graph shows the function f(x) = |x - h| + k. What is the value of k?

A k = -2.5

Over which interval is the graph of the parent absolute value function f(x)= |x| decreasing?

B (-∞, 0)

On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x + 2| as a solid line?

NOT A

Which equation represents the function graphed on the coordinate plane?

B g(x) = |x + 4| - 10

The graph shows the function f(x) = |x - h| + k. What is the value of h?

NOT D (h = 3.5)

On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x| - 4 as a solid line?

A

Which functions have a vertex with a x-value of 0? Select three options.

1. f(x) = |x| 2. f(x) = |x| + 3 4. f(x) = |x| − 6

What is the range of the function g(x) = |x - 12| - 2?

B {y | y > -2}

The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

C The range changes from {y | y > 0} to {y | y > 2}.