Problem preview
F-IF.7.b Warmup M3-024-A07-V01

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Write an equation for a transformed square-root or cube-root graph from key features

Problem

Write the square-root equation with endpoint \((4,~1)\) that passes through \((5,~3)\).

Big Picture

What this problem is really about

Use the square-root endpoint to fix the horizontal and vertical shifts immediately. Substituting the other marked point then leaves only the vertical scale factor to determine, with a particularly simple radical input. Check the resulting rule against both plotted points so the shift signs and scale cannot drift apart.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-IF.7.b
Category
Functions
Domain
Interpreting Functions
Objective
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type
Write an equation for a transformed square-root or cube-root graph from key features