Honors Precalculus Project: Transformations of Functions

Given the square root function, f(x) = √x, write a new function which illustrates a set of transformations of the original function. Your new function must include each of the following transformations:

  1. a vertical translation
  2. a horizontal translation
  3. a reflection over the x- or y-axis

Graph both functions on the same set of axes, using a different color for each of the 2 functions. On the graph write the equations of the functions using the corresponding color. Be sure to graph at least 3 actual points for each function, and label the coordinates of these points on the graph.

Write a 3 paragraph essay describing, in detail, the methods used in performing each of the transformations. Your essay must be submitted through Turnitin, and a hard copy must be included in your project.

Assemble your project as follows:

  1. Typed cover page
  2. Graphs
  3. Typed essay
  4. Rubric

Your project grade will be based on the attached rubric.

Project Due: ______

*Please note: 10 points will be deducted for each day late, including weekends!

Transformations of Functions Project Rubric

4 / 3 / 2 / 1
Transformation Equation / Includes 3 transformations / Includes 2 transformations / Includes 1 transformation / Includes no transformation
Graph of f(x)=√x / No errors / Contains 1 minor error / Contains 2 minor errors / Contains 3 or more errors
Graph of transformed f(x) / No errors / Contains 1 minor error / Contains 2 minor errors / Contains 3 or more errors
Coordinates of graphed points / No errors / Contains 1 minor error / Contains 2 minor errors / Contains 3 or more errors
Content of essay / Explanation detailed and clear, no errors / Lacks 1-2 details or contains 1-2 minor errors / Lacks 3-4 details or contains 3-4 minor errors / Contains insufficient detains or major errors
Project details / Used 2 colors in graph, equations written of graph, 3 paragraphs, neat appearance, includes typed cover page / Missing 1 detail / Missing 2 details / Missing 3 details

Project Due: ______

*Please note: 10 points will be deducted for each day late, including weekends!

Name: ______Score: ______/ 24 points