Algebra 2 Transformations of Functions Test Solutions and Scoring (PDF)

Left 2 and down 5.

Vertex (-2, -5)

Scoring: 1 point for each shift, or 1 point for the shifts and 1 point for the vertex.

Reflection: \(-x^{2}\). Up 4: \(+4\).

\(g(x) = -x^{2} + 4\)

Scoring: 1 point for the reflection, 1 point for the shift.

Left 1: each x decreases by 1. Stretch: each y is doubled.

\((-1, 3) \text{ becomes }(-2, 6)\); \((0, -1) \text{ becomes }(-1, -2)\); \((2, 2) \text{ becomes }(1, 4)\); \((4, 6) \text{ becomes }(3, 12)\).

(-2, 6), (-1, -2), (1, 4), (3, 12)

Scoring: 1 point for the horizontal shift, 1 point for the vertical stretch, 1 point for the four points.

The graph opens down (reflection), with vertex \((-1, 4)\): left 1, up 4.

\(g(x) = -|x + 1| + 4\)

Scoring: 1 point for the reflection, 1 point for the shifts.

1. \(f(-x) = x^{4} + 2x^{2} = f(x)\): even.

2. \(g(-x) = -x^{3} + 2x = -g(x)\): odd.

(a) even; (b) odd

Scoring: 1 point for each part.

Right 3, stretch by 2, down 4. \(g(7) = 2\sqrt{4} – 4 = 0\).

Domain \(x \ge 3\); range \(y \ge -4\).

g(7) = 0; domain x ≥ 3; range y ≥ -4

Scoring: 1 point for the transformations, 1 point for g(7), 1 point for the domain and range.

\(f(-4) = -4 + 3 = -1\); \(f(0) = 3 – 0 = 3\); \(f(5) = 3 – 5 = -2\).

-1, 3, -2

Scoring: 1 point for the correct piece choice, 1 point for the three values.

Reflect over the x-axis, right 4, up 16. Maximum 16 ft at \(x = 4\).

Ground: \((x – 4)^{2} = 16\), so \(x = 0\) or \(8\).

Maximum 16 ft; width 8 ft

Scoring: 1 point for the transformations and maximum, 1 point for the width.

Subtracting 4 after the function changes every output by -4, so the graph moves down 4. A left shift would be \(f(x + 4)\).

The graph moves down 4

Scoring: 1 point for the correct direction, 1 point for the explanation.