Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Which is the graph of the function  ?
|
|
|
2.
|
In the following graph, which transformations must be applied to the blue curve
to obtain the red curve?  A | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the right | B | a reflection in the x-axis, a vertical
translation of 3 units up, and a horizontal translation of 4 units to the right | C | a reflection in the
x-axis, a vertical translation of 3 units down, and a horizontal translation of 4 units to the
right | D | a reflection in the x-axis, a vertical translation of 4 units up, and a
horizontal translation of 3 units to the left |
|
|
|
3.
|
The equation of the inverse of  is
|
|
|
4.
|
Compared to the graph of the base function  , the graph of the
function  is translated A | 9 units to the left | C | 9 units down | B | 9 units to the right | D | 9 units up |
|
|
|
5.
|
Compared to the graph of the base function  , the graph of the
function  is translated A | 9 units to the right | C | 9 units down | B | 9 units up | D | 9 units to the
left |
|
|
|
6.
|
What is the equation of the transformed function, g( x), after the
transformations are applied to the graph of the base function  , shown in blue, to
obtain the graph of g( x), shown in red? 
|
|
|
7.
|
The function  represents a transformation that can best be described as
A | a reflection in the x-axis | C | a reflection in the
y-axis | B | a reflection in the x-axis and the y-axis | D | a reflection in the line y =
x |
|
|
|
8.
|
When a function is reflected in the x-axis, the coordinates of point
(x, y) become
A | (x, –y) | C | (–x, –y) | B | (–x,
y) | D | (x,
y) |
|
|
|
9.
|
What are the coordinates of the invariant point(s) when the function  is
reflected in the y-axis? A | (2, –2) | C | (0, –2) | B | (–2, 0) and (2, 0) | D | (0, 2) |
|
|
|
10.
|
Compared to the graph of the base function  , the graph of the function
 is translated A | 9 units to the left and 4 units down | C | 9 units to the right and 4 units
up | B | 4 units to the left and 9 units down | D | 4 units to the right and 9 units
up |
|
Short Answer
|
|
|
1.
|
For each g( x), describe, in the appropriate order, the combination
of transformations that must be applied to the base function  . a)  b)  c) 
|
|
|
2.
|
For each of the following, describe the combination of transformations that must
be applied to the graph of  (shown in blue) to obtain the graph of g( x)
(shown in red). a)  b)  c) 
|
Problem
|
|
|
1.
|
To rent a cottage for the months of July and August, the renter must pay a flat
fee of $150 plus a daily amount of $100.
a) Write a function that represents the total
cost, C, in dollars, of the rental as a function of the number of days, d, that the
cottage is rented.
b) Determine the domain and range of the function.
c) In the
months of November and December, the renter only needs to pay a flat fee of $50, but the daily fee is
still $100. Write a function that represents the total cost, T, in dollars, as a function of
the number of days, d, of the rental.
d) Describe a transformation that relates the
function C(d) to the function T(d).
|
|
|
2.
|
Draw a graph to determine the invariant points of  when it is reflected in
the a) x-axis b) y-axis
|
|
|
3.
|
Given the function  , a) determine the inverse of the
function b) graph the function and its inverse on the same set of axes
|