Target Equation
\(g(x) = -2x + 5\)
Worked Reasoning: Reflection + vertical stretch gives slope \(m = -2\). The line crosses the y-axis at \((0, 5)\), confirming 5 units upward vertical shift: \(g(x) = -2x + 5\).
Continued on Page 2 for Solutions 5 – 8 (3 Transformations Each) →
Teacher Resource • Complete Solutions Page 2 of 2
Problems 5 – 8 Solutions
Rubric per problem (1 pt total): 0.25 pt slope/intercepts, 0.25 pt identified transformations, 0.5 pt correct equation. 8 Points Total
5 Problem 5 Solutions
3 Transformations
Slope: m = -1/2 (-0.5)
y-int: (0, -2)
Identified Transformations (3):
Target Equation
\(g(x) = -\frac{1}{2}x - 2\) or \(-\frac{1}{2}(x + 4)\)
Worked Reasoning: Unambiguous 3-part analysis: negative slope indicates reflection (\(-\)); slope magnitude is \(1/2\) (compression); line crosses at \((0, -2)\) (shift down 2). Alternatively, shift left 4: \(-\frac{1}{2}(x+4)\).
6 Problem 6 Solutions
Fraction Slope: -2/3
Slope: m = -2/3
y-int: (0, 2)
Identified Transformations (3):
Target Equation
\(g(x) = -\frac{2}{3}x + 2\) or \(-\frac{2}{3}(x - 3)\)
Worked Reasoning: Falls 2 units for every 3 units run (\(m = -\frac{2}{3}\)). The line crosses the y-axis at \((0, 2)\), indicating translation 2 units up: \(g(x) = -\frac{2}{3}x + 2\).
7 Problem 7 Solutions
Fraction Slope: -1/3
Slope: m = -1/3
y-int: (0, 2)
Identified Transformations (3):
Target Equation
\(g(x) = -\frac{1}{3}x + 2\) or \(\frac{1}{3}(-x) + 2\)
Worked Reasoning: Points at \((-3, 3)\) and \((0, 2)\) give \(m = -\frac{1}{3}\). Upward shift of 2 units gives constant \(+2\), yielding \(g(x) = -\frac{1}{3}x + 2\).
8 Problem 8 Solutions
Fraction Slope: -3/2
Slope: m = -3/2 (-1.5)
y-int: (0, -1)
Identified Transformations (3):
Target Equation
\(g(x) = -\frac{3}{2}x - 1\) or \(-1.5x - 1\)
Worked Reasoning: Falls 3 units for every 2 units run (\(m = -\frac{3}{2} = -1.5\)). Crosses y-axis at \((0, -1)\), showing downward shift of 1: \(g(x) = -\frac{3}{2}x - 1\).
Fraction Slopes Coverage: Problems 3 (\(1/2\)), 5 (\(-1/2\)), 6 (\(-2/3\)), 7 (\(-1/3\)), and 8 (\(-3/2\)) assess both proper and improper fraction slopes under reflections and shifts.
