
Directions: Read carefully. Choose the best answers.
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 xaxis, and then translating the graph up four units.




2. 
The graph of f ( x) is shown at the right on the domain [3,3].
A function k ( x) is defined as
k ( x) = f ( x + 1)  2.
Sketch the graph of k (x).





3. 
Describe the transformations that would produce the graph of the second function from the graph of the first function, for sections a, b and c.




4. 
Given the graph of the function
f (x) shown at the right on the interval [0,6].
Sketch the graphs of:
a. f (x + 1)
b. f (x)  2
c. f (x)
d. f (x)
e. 2 f (x) 




5. 
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.




6. 
Transform the function f (x) = e^{x} with a vertical stretch by a factor of 3, followed by a translation 5 units to the right.
a. Write an equation for the transformed function.
b. Graph the transformed function.




7. 
Write the equation for the graph shown at the right. The line segments shown are straight and intersect at the point (4,2). The xintercepts are (2,0) and (6,0).
Assume that the parent function was
y =  x .




8. 
Given: f (x) = x^{2}  2x
a. Determine an expression for h(x), if h(x) = f (x).
b. Determine an expression for g(x), if g(x) is represented by the rotation of 180º of f (x) about the origin.
c. Rotate f (x) 90º about the origin. Find the coordinates of the point(s)
for which x = 1, under the rotation.



9. 
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? 


10. 
A function is defined as f (x) = x^{3}  4.
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.



11. 
Given: the function shown at the right y = x( x  2)( x + 3)
a. Graph the given function with a vertical stretch of factor ½ and a translation of 3 units to the left.
b. Graph the given function with a translation of 6 units to the right.
c. Describe the transformation that occurred to the given function, if a new function's equation is
y = 4 x( x  2)( x + 3).
d. Describe the transformation that occurred to the given function, if a new function's equation is 


12. 
Given: function, y = x^{2}  1 graphed in blue.
Match the transformation equations shown below with their corresponding graphs.
Possible equation matches (not in matching order):
(1) y = 2 (x^{2}  1)
(2) y = ½ (x^{2}  1)
(3) y = (½ • x)^{2}  1




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