This algebra 2 transformations test answer key gives the full solution and the scoring guide for each of the 9 test questions on transformations of functions.
Use this key to score the test out of 20 points. Each solution shows the full work, and the scoring note explains how the points are awarded. Accept equivalent equations and any correct graph through the listed points.
Algebra 2 Transformations Test Answer Key: questions 1–5
Question 1: Shifts of absolute value (2 points)
- Shifted left 3 and down 5.
- Vertex: \((-3,-5)\).
Scoring: 1 point for each correct direction pair in (a), accepting ‘left 3, down 5’ only with both parts; 1 point for the vertex.
Question 2: Transform points (2 points)
- Subtract 3 from each x-coordinate: \((-7,2),(-3,-3),(3,5)\).
- Double each y-coordinate: \((-4,4),(0,-6),(6,10)\).
Scoring: 1 point per part, all three points correct.
Question 3: Write an equation (2 points)
- \(g(x)=-(x-2)^{2}+7\).
- \(g(5)=-(3)^{2}+7=-9+7=-2\).
Scoring: 1 point for the equation; 1 point for the value.
Question 4: Even and odd (3 points)
- \(f(-x)=2x^{4}-x^{2}=f(x)\): \(\text{even}\).
- \(g(-x)=-x^{3}+5x=-g(x)\): \(\text{odd}\).
- \(h(-x)=x^{2}-3x\), not equal to \(h(x)\) or \(-h(x)\): \(\text{neither}\).
Scoring: 1 point per part for the correct classification supported by computing \(f(-x)\).
Question 5: Graph a square root (3 points)
The start is \((-1,-2)\). Points: \((-1,-2),(0,-1),(3,0),(8,1)\).
Domain: \(x\ge -1\). Range: \(y\ge -2\).
Scoring: 1 point for the correct starting point; 1 point for a correct curve through at least three points; 1 point for domain and range.
Algebra 2 Transformations Test Answer Key: questions 6–9
Question 6: Cube root from a graph (2 points)
The curve flattens at its center \((1,3)\), so \(h=1\) and \(k=3\). Check \((9,5)\): \(\sqrt[3]{8}+3=5\). Equation: \(y=\sqrt[3]{x-1}+3\).
Scoring: 1 point for identifying the center; 1 point for the equation.
Question 7: Stretch and reflect (2 points)
- Vertical compression by \(\frac{1}{2}\), reflection over the x-axis, and a shift up 4.
- \(g(6)=-\frac{1}{2}(6)+4=-3+4=1\).
Scoring: 1 point for naming all three transformations; 1 point for the value.
Question 8: Exponential graph (2 points)
- The parent \(2^{x}\) has asymptote \(y=0\); shifting down 4 gives \(y=-4\).
- \(2^{x}=4\) gives \(x=2\): \((2,0)\).
Scoring: 1 point per part.
Question 9: Skid speed (2 points)
- \(s(24)=\sqrt{576}=24\) mph.
- \(36=\sqrt{24d}\) gives \(1296=24d\) and \(d=54\) feet.
Scoring: 1 point per part.
Scoring summary
20 points: add the points of every question of this algebra 2 transformations test answer key.
How to use this algebra 2 transformations test answer key
Use this algebra 2 transformations test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Algebra 2 Transformations of Functions test answer key
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