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Given a graph of some function f, the student is asked for values of \$f\$ and its inverse. Function is cubic and invertible.

"}, "ungrouped_variables": ["a", "hshift", "vshift", "x1", "x2", "y1", "y2"], "variables": {"hshift": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "hshift", "description": "

Random amount of horizontal shift to create variability.

"}, "x1": {"definition": "random(0..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "x1", "description": ""}, "y1": {"definition": "a*((x1+hshift)^3+(x1+hshift)+vshift)", "templateType": "anything", "group": "Ungrouped variables", "name": "y1", "description": ""}, "vshift": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "vshift", "description": "

Random amount of vertifical shift for sake of variability.

"}, "x2": {"definition": "random(-1..1 except x1)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "y2": {"definition": "a*((x2+hshift)^3+(x2+hshift)+vshift)", "templateType": "anything", "group": "Ungrouped variables", "name": "y2", "description": ""}, "a": {"definition": "random(-1..1 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": "

Coefficient of x^3

{eqnline(a, hshift, vshift)}

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Above is the graph of some function \$f\$.

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What is \$f(\\var{x1})\$? [[0]]

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What value of \$x\$ do you need to get \$f(x) = \\var{y2}\$? [[1]]

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What is \$f^{-1}(\\var{y2})\$? [[2]]