Trigonometric Functions

The following transformations š‘¦ = 3š‘“ (1 š‘„ āˆ’ 2šœ‹) āˆ’ 1 were applied to the parent function f(x) = csc(x). Graph the transformed function for the interval āˆ’4šœ‹ ā‰¤ š‘„ ā‰¤ 4šœ‹. On your graph, label the asymptotes, local max/min, and number each axis. Use mapping notation to show your work for a minimum of 5 key points for full marks.

I'm having a lot of trouble with the local max/min and the 5 key points, could anyone help me? Please and thank you.

  1. 👍
  2. 👎
  3. 👁
  1. csc(x) has asymptotes, with their local branch turning points at min = 1 and max = -1
    so, 3f(x-2Ļ€)-1 has its turning points at 3-1 and -3-1
    Note also that since the period of csc(x) is 2Ļ€, shifting right by 2Ļ€ does not change the graph in any way. So your graph will still cover exactly four periods. The turning points are all just shifted down by 1. There are still no x-intercepts.

    The only real key points for csc(x) are the asymptotes at x = kĻ€, and the turning points at x = odd multiples of Ļ€/2. That is at x = kĻ€ + Ļ€/2

    1. 👍
    2. 👎
    👤
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    12. To describe a sequence of transformations that maps triangle ABC onto triangle A''B''C'', a student starts with a reflection x-axis. `How should the student complete a sequence of transformations to map ABC onto triangle

  2. college algebra

    find the function that is finally graphed after the following transformations are applied to the graph of y=sqrt x in the order listed. 1. relected about the x-axis 2. shift down 9 units 3. shift left 2 units y=

  3. Math - Int Trig

    Write an equation for the function that is finally graphed after the following transformations are applied to the graph y=|x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and

  4. trig

    . The following transformations y=3f(1/2x-2pi)-1 were applied to the parent function f(x)=csc(x). Graph the transformed function for the interval āˆ’ 4Ļ€ ā‰¤ š‘„ ā‰¤ 4Ļ€. On your graph, label the asymptotes, local max/min, and

  1. Physics

    A force of 32 N is applied at the end of a wrench handle that is 27 cm long. The force is applied in a direction perpendicular to the handle as in the diagram. (a) What is the torque applied to the nut by the wrench? (b) What

  2. math

    Consider the equation f(x)= -2 sqrt(X+3). List in order the transformations applied to the parent function.

  3. physics

    Two boxes are seen to accelerate at the same rate when a force F is applied to the first and 5 F is applied the second. What is the mass ratio of the first box to the second?

  4. Math

    To describe a sequence of transformations that maps triangle ABC onto triangle A''B''C'', a student starts with a reflection over the x-axis. How should the student complete the sequence of transformations to map triangle ABC onto

  1. Advanced Functions

    Given the functions š‘“(š‘„) = š‘™š‘œš‘”_3 (3š‘„) and š‘”(š‘„) = š‘™š‘œš‘”_3 (š‘„) + 1 a. Describe the transformations applied to each function. b. How do the graphs of the two functions compare? Explain your answer by

  2. Trigonometric Functions

    The following transformations š‘¦ = 3š‘“ (1/2 š‘„ āˆ’ 2šœ‹) āˆ’ 1 were applied to the parent function f(x) =csc(x). Graph the transformed function for the interval āˆ’4šœ‹ ā‰¤ š‘„ ā‰¤ 4šœ‹. On your graph, label the

  3. Trigonometric Functions

    The following transformations š‘¦ = 3š‘“ (1/2 š‘„ āˆ’ 2šœ‹) āˆ’ 1 were applied to the parent function f(x) = csc(x). Graph the transformed function for the interval āˆ’4šœ‹ ā‰¤ š‘„ ā‰¤ 4šœ‹. On your graph, label the

  4. Math-functions

    A function, y = f(x), originally has a domain of x equal or bigger than 4 and a range of y equal or smaller than 1. Determine the new domain and range of y=-2f(-x+5)+1 after applying all transformations. (Hint: Sketch the

You can view more similar questions or ask a new question.