Function Transformations Test – Algebra 2 Math (Printable PDF)

Question 1 Describe a transformation (2 points)

Describe the graph of g(x) = −2(x + 4)² − 5 as a transformation of f(x) = x², and give the vertex.

Question 2 Write an equation (2 points)

Write the equation of the cube root function obtained from f(x) = ∛x by a vertical stretch by 4, a shift right 5, and a shift up 3.

Question 3 Even or odd (3 points)

Classify each function as even, odd, or neither, and show the work.

1. f(x) = x⁶ − 2x² (1 point)
2. g(x) = x⁵ + 4x³ (1 point)
3. h(x) = x³ + x² (1 point)

Question 4 Square root graph (3 points)

The graph of a square root function is shown with the points (−2, −3), (−1, −2), and (2, −1).

1. Write its equation. (1 point)
2. State the domain. (1 point)
3. State the range. (1 point)

Question 5 An exponential transformation (3 points)

Let g(x) = 3^{x + 2} − 4 and f(x) = 3^x.

1. Describe the transformation from f to g. (1 point)
2. Give the equation of the horizontal asymptote of g. (1 point)
3. Find the y-intercept of g. (1 point)

Question 6 Transform a graph (3 points)

The graph of f consists of segments joining (−3, 0), (−1, 2), (1, −1), and (3, 1).

1. List the vertices of g(x) = f(x + 2) − 1. (2 points)
2. List the vertices of h(x) = −f(x). (1 point)

Question 7 Profit model (2 points)

A bakery’s daily profit, in dollars, is P(n) = −(n − 40)² + 900 when n cakes are sold. Describe P as a transformation of n², and state the greatest profit and the number of cakes that gives it.

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

For f(x) = x², let g(x) = f(2x). Show that g(x) = 4x², and give the point of g that matches the point (2, 4) of f.