Function Transformations Test Answer Key with Scoring – Algebra 1

Question 1 Shift a Parabola (2 points)

+5 inside moves the graph 5 units left, and −4 outside moves it 4 units down.

Left 5, down 4; vertex (−5, −4)

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

Question 2 Read an Absolute Value Rule (2 points)

Vertex (3, 6). The coefficient is negative, so it opens down. |−12| < 1, so the graph is wider.

Scoring: 1 point for the vertex, 1 point for direction and width.

Question 3 Move a Point (2 points)

1. (4, −2 + 3) = (4, 1).
2. The shift is 1 unit right: (5, −2).

Scoring: 1 point per part.

Question 4 Evaluate a Piecewise Function (3 points)

1. −3 < −1: 2(−3) + 3 = −3. 0 is in [−1, 2]: 0 − 4 = −4.
2. 2 is in [−1, 2]: 4 − 4 = 0.
3. 5 > 2: 6 − 5 = 1.

Scoring: 1 point per part; both values are needed in part (a).

Question 5 Absolute Value Graph (3 points)

1. (−2, 3).
2. h = −2 and k = 3. Use (0, 1): 1 = a|2| + 3, so a = −1. y = −|x + 2| + 3
3. −|x + 2| + 3 = 0 gives |x + 2| = 3, so x = 1 and x = −5.

Scoring: 1 point per part.

Question 6 Shipping Steps (2 points)

1. At 3 pounds the closed circle is at height 12: $12.
2. 1.5 lies in the step 1 < w ≤ 2, so $9.

Scoring: 1 point per part.

Question 7 Phone Data Plan (3 points)

1. C(g) = 25 for 0 ≤ g ≤ 3; C(g) = 25 + 8(g − 3) for g > 3.
2. 25 + 8(2.5) = 25 + 20 = $45.

Scoring: (a) 1 point per piece. (b) 1 point.

Question 8 Write a Transformed Parabola (3 points)

1. Right 6: (x − 6)². Reflect: −(x − 6)². Up 2: y = −(x − 6)² + 2.
2. Vertex (6, 2). At x = 8: −(2)² + 2 = −2.

Scoring: (a) 1 point for the horizontal and reflection steps, 1 point for the vertical shift. (b) 1 point.