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Name:Date:School: Facilitator: 1.07 Absolute Value Functions This task requires you to create a graph. You have several options: • Use the word tools; • Draw the graph by hand, then photograph or scan your graph; or • Use the GeoGebra linked on the Task page of the lesson to create the graph, then insert a screenshot of the graph into this task. Determine the vertex of each absolute value function, state whether the vertex is a maximum or minimum point, determine the opening of the graph, graph each function, and describe the translation. 1.f(x) = |x| – 4 Vertex:-4,0Maximum or minimum?: min Opens:
Describe the translation: down 4 2.f(x) = -|x– 5| + 3 Vertex:(0,-2)Maximum or minimum?: max Opens: Describe the translation:reversed, up 2, right 4.5
3.f(x) = |x+ 2| – 3 Vertex:(0,-1)Maximum or minimum?: min Opens: Describe the translation:down 3 left 1
4.f(x) = -|x– 2| – 3 Vertex:(0,-5)Maximum or minimum?: max Opens: Describe the translation:down 3 right 2 reversed
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Unformatted text preview:5. When comparing the graph of g(x) and the equation of f(x), which function has a larger maximum? Explain why. g(x) f(x) 6. If and the graph of h(x) translates right 3 and up 2, which function has a smaller minimum? Explain why. 7. Rewrite as a piecewise function. f ( x ) = − x + 4 − 5 f ( x ) = x − 2 + 1 f ( x ) = x f ( x ) = { FORMTEXT , x < FORMTEXT FORMTEXT , x ≥ FORMTEXT Use the GeoGebra linked on the task page to solve the next three problems. 8. Solve |2 x-6| = 4 x +4| Answer: Copy and paste a picture of your graph below: 9. |3 x +6| = |-9 x-12| Answer: Copy and paste a picture of your graph below: 10. The cost of shipping a 25-lb. box with UPS is $25.50. If the weight, w, of the box may vary by no more than 3 pounds, what is the range of weights of a box that ships for $25.50? Equation: Answer: Copy and paste a picture of your graph below: