Transformation of Graphs Worksheet

Transformation of Graphs

Read each question carefully and provide your answer in the space provided. Show all your work for full credit.

1. If the graph of y = f(x) is shifted 3 units to the right and 2 units up, what is the equation of the new graph?

2. Which transformation changes the orientation of a graph?

3. A vertical stretch of the graph y = f(x) by a factor of 'a' results in the equation y =  .

4. The graph of y = -f(x) represents a   over the x-axis.

5. A horizontal compression of y = f(x) by a factor of 'b' (where b > 1) results in y = f( ).

6. Describe the transformations applied to the graph of y = x² to obtain the graph of y = -2(x + 1)² - 3.

7. Given the function f(x) = |x|, write the equation of the function g(x) that is a reflection across the y-axis, followed by a vertical stretch by a factor of 4, and then a translation 5 units down.

8. The order of transformations (translations, reflections, stretches/compressions) does not affect the final graph.

9. A horizontal stretch by a factor of 'k' (k > 1) means the graph gets wider.

10. Graph the function g(x) = -(x - 2)² + 1 on the coordinate plane below. The parent function is f(x) = x².