Assessment: Absolute Value Functions
Answer every question, then submit to see your score and which topics to review.
Part A — Concept Questions
What shape does y = |x − h| + k always make?
EasyWhat does a negative a do to the graph of y = a|x|?
EasyPart B — Formula & Application
What is the vertex of y = 3|x − 2| + 5?
MediumSolve |x − 10| = 3 for the smaller solution.
MediumPart C — Problem Solving
Solve |x − 6| ≤ 2.
HardWhat is the maximum value (the y-coordinate of the vertex) of y = −|x − 7| + 9?
MediumPart D — Real-Life Application
A bolt must be within 0.2 mm of a target 15 mm diameter. The acceptable boundary is |diameter − 15| = 0.2. What are the boundary diameters?
MediumA greenhouse alarm triggers when |temperature − 22| > 4 (°C). Which readings trigger the alarm?
MediumPart E — Challenge
A V-shaped graph has vertex (3, −2) and passes through (5, 4). What is a? (Use y = a|x−3| − 2.)
HardSolve 2|x − 4| − 6 = 0 for the larger solution. (Hint: first isolate the absolute value.)
Hard0/10 answered