Math Quiz

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  • Topic: Trigonometric functions, Trigonometry, Inverse function
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Math 30 – 1 – Final Exam Review BookletName:________________________________ Chapter 1 (Transformtions) Review

Multiple Choice
For #1 to #6, choose the best answer.
1.The graph y  f (x) contains the point (3, 4). After a transformation, the point (3, 4) is transformed to (5, 5). Which of the following is a possible equation of the transformed function?
Ay  1  f (x  2)
By  1  f (x  2)
Cy  1  f (x  2)
Dy  1  f (x  2)
2.The graph of y   x  is transformed by a vertical stretch by a factor of 3 about the x-axis, and then a horizontal translation of
3 units left and a vertical translation up
1 unit. Which of the following points is on the transformed function?
A(0, 0)
B(1, 3)
C(3, 1)
D(3, 1)
3.The graph of is vertically stretched by a factor of 2 about the x-axis, then reflected about the y-axis, and then horizontally translated left 3. What is the equation of the transformed function?

A
B
C
D
4.Which of the following transformations would produce a graph with the same x-intercepts as y  f (x)?
Ay  f (x)
By  f (x)
Cy  f (x  1)
Dy  f (x)  1

5.Given the graph of y  f (x), what is the invariant point under the transformation y  f (2x)?

A(1, 0)B(0, )
C(1, 1)D(3, 1)
6.What will the transformation of the graph of y  f (x) be if y is replaced with y in the equation y  f (x)?
AIt will be reflected in the x-axis.
BIt will be reflected in the y-axis.
CIt will be reflected in the line y  x.
DIt will be reflected in the line y  1.
Short Answer
7.If the range of function y  f (x) is {y  y 4}, state the range of the new function g(x)  f (x  2)  3.
8.As a result of the transformation of the graph of y  f (x) into the graph of y  3f (x  2)  5, the point (2, 5) becomes point (x, y). Determine the value of (x, y).
9.The graph of f (x) is stretched horizontally by a factor of about the y-axis and then stretched vertically by a factor of about
the x-axis. Determine the equation of the transformed function.
10.A function f (x)  x2  x  2 is multiplied by a constant value k to create a new function g(x)  k f (x). If the graph of y  g(x) passes through the point (3, 14), state the value of k.

Extended Response
11.Sketch the graph of the inverse relation.
b)
b)
a)

a) If the point (1, 1) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

b)If the point (4, 2) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

b) If the point (1, 1) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

b)If the point (4, 2) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

12.The graphs of y  f (x) and y  g(x) are shown.

13.Consider the graph of the function y  f (x).
a) Describe the transformation of
y  f (x) to y  3f (2 (x  1))  4.

b)Sketch the graph.

b) Describe the transformation of
y  f (x) to y  3f (2 (x  1))  4.

b)Sketch the graph.

14.A function is defined by
f (x)  (x  2)(x  3).
a)If g(x)  kf (x), describe how k affects the y-intercept of the graph of the function y  g(x) compared to y  f (x).
b)If h(x)  f (mx), describe how m affects the x-intercepts of the graph of the function y  h(x) compared to y  f (x).

15.Complete the following for the quadratic function f (x)  x2  2x  1.
a)Write the equation of f(x)...
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