Absolute Value Functions Answers
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What are the domain and range of the function?
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What are the domain and range of the function?
Which of the following is a horizontal stretch of the parent function?
Which graph shows f(x) = 0.5|x + 3| – 2?
Which graph shows f(x) = |x| reflected across the x-axis, translated 2 units down and 1 unit to the left?
Which equation represents the reflected and translated function? f(x) = –|x – 2| – 1✔ f(x) = –|x + 1| – 2 f(x) = |x + 2| – 1
Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?
Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6?
What are the acceptable diameters for the golf balls?
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?X f(x) = |x – 42.67|✔ f(x) = |42.67 – x|f(x) = |42.67 + x|
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.
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).
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