Transformations of Functions: Algebra 2 Math Test Answer Key – PDF Download

Question 1: Shifts of absolute value (2 points)

1. Shifted left 3 and down 5.
2. 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)

1. Subtract 3 from each x-coordinate: \((-7,2),(-3,-3),(3,5)\).
2. 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)

1. \(g(x)=-(x-2)^{2}+7\).
2. \(g(5)=-(3)^{2}+7=-9+7=-2\).

Scoring: 1 point for the equation; 1 point for the value.

Question 4: Even and odd (3 points)

1. \(f(-x)=2x^{4}-x^{2}=f(x)\): \(\text{even}\).
2. \(g(-x)=-x^{3}+5x=-g(x)\): \(\text{odd}\).
3. \(h(-x)=x^{2}-3x\), 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.

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)

1. Vertical compression by \(\frac{1}{2}\), reflection over the x-axis, and a shift up 4.
2. \(g(6)=-\frac{1}{2}(6)+4=-3+4=1\).

Scoring: 1 point for naming all three transformations; 1 point for the value.

Question 8: Exponential graph (2 points)

1. The parent \(2^{x}\) has asymptote \(y=0\); shifting down 4 gives \(y=-4\).
2. \(2^{x}=4\) gives \(x=2\): \((2,0)\).

Scoring: 1 point per part.

Question 9: Skid speed (2 points)

1. \(s(24)=\sqrt{576}=24\) mph.
2. \(36=\sqrt{24d}\) gives \(1296=24d\) and \(d=54\) feet.

Scoring: 1 point per part.

⬇ Download the Algebra 2 Transformations of Functions test answer key (PDF, 106 KB)

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