Question

3. Your friend attempted to describe the transformations applied to the graph of y- sinz to give the equation

+30))+1. They think the following transformations have been applied. Which transformatic
have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(z) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
3. Describe in words, the transformations you would apply to f(x) = cosz to produce g(x) = -3cos((x +45))

Answer 1

E is correct

Explanation:

a) The statement that f(x) has been reflected vertically is incorrect. A vertical reflection would change the sign of the function, but the given equation, "+30))+1," does not indicate any reflection.

b) The statement that f(z) has been stretched vertically by a factor of 2 is incorrect. If the function were stretched vertically by a factor of 2, the equation would include a multiplication by 2, such as "+2" or "×2." However, the given equation, "+30))+1," does not indicate any vertical stretching.

c) The statement that f(x) has been stretched horizontally by a factor of 3 is incorrect. If the function were stretched horizontally by a factor of 3, the equation would include a division by 3 or a multiplication by 1/3. However, the given equation, "+30))+1," does not indicate any horizontal stretching.

d) The statement that f(x) has a phase shift left 30 degrees is incorrect. A phase shift is typically represented by a horizontal translation, and the given equation, "+30))+1," does indicate a horizontal translation but not by 30 degrees. Instead, it suggests a horizontal translation of 30 units to the left.

e) The statement that f(x) has been translated up 1 unit is correct. The equation, "+30))+1," indicates a vertical translation of 1 unit upward.

In summary, the correct identification is:

a) Incorrect

b) Incorrect

c) Incorrect

d) Incorrect

e) Correct