Working with Transformations and Functions
 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Grab your graphing calculator and investigate
the following problems relating to functions.
(Answers will be given using the TI-83+/84+.)

1.

Write the equation for the graph of function g(x), obtained by shifting the graph of
 f (x) = x²
 three units left, stretching the graph vertically by a factor of two, reflecting that result over the x-axis, and then translating the graph up four units.
 

Answer

 

 

2.

Describe the transformations that would produce the graph of the second function from the graph of the first function.


 
 

Answer

 

 

3.

Given the graph of the function f (x) shown below, sketch the graphs of:

a.  f (x + 1)

b. f (x) - 2

c. f (-x)

d. -f (x)

e. 2 f (x)
 

Answer


 

 

4. A function is an odd function when f (-x) = -f (x).  Graphs of odd functions are symmetric with respect to the origin.
A function is an even function when f (-x) = f (x).  Graphs of even functions are symmetric with respect to the y-axis.

Determine if the functions f (x) and g(x) shown below are odd, even or neither:
                                             

 

Answer for f (x)                            Answer for g(x)

 

 

5.

A function is defined as

Sketch the graph of f (x) and f -1 (x) on the same axis and describe in transformational terms the relationship between these two graphs.

 

Answer

 

 

6.

Let x represent the length of a side of a square and an edge of a cube.

a.  Graph the area of the square as a function of x.

b.  On the same axes, graph the surface area of the cube as a function of x.

c.  Describe the relationship between these two graphs using transformational
     terms.

 

Answer

 

 

7.

 

Write the equation for the graph shown at the right.  Assume that the parent function was
.

 

Answer

 

 

8.

Consider the relationship between Fahrenheit and Celsius temperatures.  Using your graphing calculator, graph these two functions on the same set of axes:
                     
a.  Describe in transformational terms, how the first graph becomes the second graph.

b.  At what temperature are the Fahrenheit and Celsius readings the same?
 

Answer