Function Transformations Test – Algebra 1 Math (Printable PDF)

Question 1 Shift a Parabola (2 points)

Describe how the graph of g(x) = (x + 5)² − 4 is related to the graph of f(x) = x², and name the vertex.

Question 2 Read an Absolute Value Rule (2 points)

For h(x) = −12|x − 3| + 6, state the vertex, whether the graph opens up or down, and whether it is wider or narrower than y = |x|.

Question 3 Move a Point (2 points)

The point (4, −2) is on the graph of y = f(x). Give the corresponding point on each graph.

1. y = f(x) + 3 (1 point)
2. y = f(x − 1) (1 point)

Question 4 Evaluate a Piecewise Function (3 points)

Let f(x) = 2x + 3 for x < −1; f(x) = x² − 4 for −1 ≤ x ≤ 2; and f(x) = 6 − x for x > 2.

1. Find f(−3) and f(0). (1 point)
2. Find f(2). (1 point)
3. Find f(5). (1 point)

Question 5 Absolute Value Graph (3 points)

The graph shows an absolute value function.

1. Name the vertex. (1 point)
2. Write an equation of the form y = a|x − h| + k. (1 point)
3. Find the x-intercepts. (1 point)

Question 6 Shipping Steps (2 points)

The graph shows the cost of shipping a package by weight.

1. What does it cost to ship a 3-pound package? (1 point)
2. What does it cost to ship a 1.5-pound package? (1 point)

Question 7 Phone Data Plan (3 points)

A plan costs $25 for up to 3 gigabytes (GB). Each GB beyond 3 costs another $8.

1. Write the cost C(g) as a piecewise function. (2 points)
2. Find the cost of using 5.5 GB. (1 point)

Question 8 Write a Transformed Parabola (3 points)

The graph of y = x² is moved 6 units right, reflected over the x-axis and moved 2 units up.

1. Write the new equation. (2 points)
2. Give the vertex and the y-value at x = 8. (1 point)