Function Transformations Test Answer Key with Scoring – Algebra 2

Question 1 Describe a transformation (2 points)

Reflect across the x-axis, stretch vertically by 2, shift left 4, and shift down 5.

Vertex (−4, −5)

Scoring: 1 point for the reflection and stretch, 1 point for the shifts and vertex.

Question 2 Write an equation (2 points)

Stretch: 4∛x. Right 5: replace x by x − 5. Up 3: add 3.

g(x) = 4∛(x − 5) + 3

Scoring: 1 point for the stretch and shift inside, 1 point for the vertical shift.

Question 3 Even or odd (3 points)

a) f(−x) = x⁶ − 2x² = f(x): even.

b) g(−x) = −x⁵ − 4x³ = −g(x): odd.

c) h(−x) = −x³ + x², which is neither h(x) nor −h(x): neither.

Scoring: 1 point each.

Question 4 Square root graph (3 points)

a) The start (−2, −3) means left 2 and down 3: y = √(x + 2) − 3. Check (2, −1): √4 − 3 = −1 ✓.

b) x ≥ −2.

c) y ≥ −3.

Scoring: 1 point per part.

Question 5 An exponential transformation (3 points)

a) Left 2 and down 4.

b) The asymptote y = 0 moves down 4: y = −4.

c) g(0) = 3² − 4 = 5.

Scoring: 1 point per part.

Question 6 Transform a graph (3 points)

a) f(x + 2) shifts left 2 and −1 shifts down 1: (−5, −1), (−3, 1), (−1, −2), (1, 0).

b) Change the sign of each y-coordinate: (−3, 0), (−1, −2), (1, 1), (3, −1).

Scoring: 2 points for g (1 for the horizontal move, 1 for the vertical move); 1 point for h.

Question 7 Profit model (2 points)

Reflect across the n-axis, shift right 40, shift up 900. The vertex is (40, 900).

Greatest profit $900 when 40 cakes are sold

Scoring: 1 point for the transformation, 1 point for the maximum and the number of cakes.

Question 8 A compression that equals a stretch (2 points)

g(x) = (2x)² = 4x².

The point (2, 4) of f becomes (1, 4) on g: the x-coordinate is halved (horizontal compression by 12).

g(x) = 4x²; point (1, 4)

Scoring: 1 point for the expansion, 1 point for the matching point.