Absolute Value Functions

Question 1

The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

Revolt · Accepted Answer

Yes, the graph has been dilated by a scale factor of 3. To determine this, use the standard form of an absolute value function, y = a|x – h| + k, where (h, k) is the vertex. Substituting the vertex (-2, 3) and the point (-1, 0) into the equation gives 0 = a|(-1) – (-2)| + 3. Simplifying this results in 0 = a(1) + 3, which means a = –3. Since the absolute value of a is 3 (not 1), the graph has undergone a vertical stretch (dilation).

Question 2

Find the vertex of the given function. f(x) = |x – 5| + 10 The vertex is at (, ).

Revolt · Accepted Answer

5

Question 3

Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at (, ).

Revolt · Accepted Answer

Part 1: -1; Part 2: -7

Question 4

Which of the following is a horizontal stretch of the parent function?

Revolt · Accepted Answer

C:

Question 5

Which graph shows f(x) = 0.5|x + 3| – 2?

Revolt · Accepted Answer

A: mc001-1.jpg

Question 6

Which graph shows f(x) = |x| reflected across the x-axis, translated 2 units down and 1 unit to the left?

Revolt · Accepted Answer

B:

Question 7

Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?

Revolt · Accepted Answer

A: x = 2, x = 8

Question 8

The standard diameter of a golf ball is 42.67 mm.A golf ball factory does quality control on the golf balls it manufactures. Golf balls are randomly measured to ensure the correct size. If the discrepancy in diameter is more than 0.004 mm, the production is stopped.Which function could represent this situation?

Revolt · Accepted Answer

A: f(x) = |x – 42.67|

Question 9

Which of the following did you include in your answer?

Revolt · Accepted Answer

A: Yes, the graph has been dilated.; B: Using the standard form of the equation, substitute in the values: h = –2, k = 3, x = –1, and y = 0.; C: Solve the equation to get a = –3.; D: Graphically, the parent function follows the pattern of right 1, up 1. Moving 1 unit to the right from the vertex, you can move down 3 units to get to the point (–1, 0), so it has been horizontally compressed.

Question 10

Question 10

Revolt · Accepted Answer

10

Absolute Value Functions Answers

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Absolute Value Functions Answers

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