Absolute Value Practice

What is the vertex of the absolute value function y = |x + 3| - 2?

• (-2, -3)

• (-3, -2)

• (0, 0)

• (3, 2)

Answer explanation

Identify the horizontal shift by finding the h, which is inside the absolute value signs (h = -3, so the shift is 3 to the left). Identify the vertical shift by finding the k, which is outside the absolute value signs (k = -2, so the shift is down 2).

Tags

CCSS.HSF-IF.C.7D

Identify the axis of symmetry for the absolute value function y = |x - 4| + 1.

• x = 4

• x = 2

• y = 2

• x = -2

Answer explanation

The absolute value function y = |x - 4| + 1 has its vertex at (4, 1). The axis of symmetry is the vertical line that passes through the vertex, which is x = 4. Thus, the correct answer is x = 4.

Tags

CCSS.HSF-IF.C.7D

Which transformation results in shifting the graph of y = |x| to the right by 4 units?

• y = |x - 4|

• y = |x + 4|

• y = |x - 4| + 4

• y = |x| - 4

Answer explanation

To shift the graph of y = |x| to the right by 4 units, we replace h, which is inside the absolute value signs, with 4. Thus, the correct transformation is y = |x - 4|.

What is the range of y = |x| ?

• y < 0

• All real numbers

• y > 0

• y > 0

Answer explanation

The function y = |x| represents the absolute value of x, which is always non-negative. Therefore, the range of y is y ≥ 0. The correct choice is y > 0, as it excludes y = 0, which is not part of the range.

What is the vertex of the function?

• (2, 0)

• (0, 2)

• (2, 2)

• (-2, 0)

Tags

CCSS.HSF-IF.C.7D

What is the equation of this graph?

• f(x) = (x + 2)² - 3

• f(x) = (x - 2)² - 3

• f(x) = |x + 2| - 3

• f(x) = |x - 2| - 3

Answer explanation

The correct equation is f(x) = |x + 2| - 3, which represents a V-shaped graph with a vertex at (-2, -3). The other options represent parabolas or different absolute value graphs, which do not match the given graph.

Tags

CCSS.HSF-IF.C.7D