posted by Alana K

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 graph&apply the transformations)

Note: I have tried many approaches to this and I am stuck. How do I solve this if I don't know what the original equation is?

  1. Steve

    If the domain of f(x) is x > 4
    then the domain of f(-x+5) is
    -x+5 > 4
    x < 1

    The range of f(x) is y <= 1
    The range of -2f(x) is y >= -2
    The range of -2f(x)+5 is y >= -2+5 or y >= 3
    Consider f(x)=-x^2+1
    -2f(x)+5 = 2x^2+3
    Using f(-x+5) does not affect the range -- it just shifts/reflects horizontally

  2. Alana K

    Thank you for response Steve. How did you get -2f(x) is y >= -2 ? I keep thinking it should be -1/2

  3. Alana K

    never mind, ignore my last comment, it's incorrect. thank you for your help.

Respond to this Question

First Name

Your Answer

Similar Questions

  1. math

    Identify the domain and range of the following: f(x) = 4-x^2, -5<x<-1 3/2x + 3/2, -1<x<3 (both "<" signs are actually less than or equal to) x+3, 3<x<10 (x<10 is actually less than or equal to) All three are …
  2. Calculus

    I'm doing graphs/domain/range of basic functions. I have three questions: How do I find the domain and range of a function?
  3. Algebra-I'm still stuck

    The one-to-one function f is defined by f(x)=(4x-1)/(x+7). Find f^-1, the inverse of f. Then, give the domain and range of f^-1 using interval notation. f^-1(x)= Domain (f^-1)= Range (f^-1)= Any help is greatly appreciated. Algebra …
  4. precalculus check immediately

    suppoe f is a function with domain [1,3]and range[2,5]?
  5. Algebra 2

    Hi, I need help finding the domain and range of the Quadratic Model on part b. I've included part a. just in case you may need it. a.The parabolic path of a thrown ball can be modeled by the table. the top of the wall is at (5,6). …
  6. Precalc (domain and range)

    Domain l(x) is -12 less than or equal to x less than equal to 12 and it's range is 0 less than or equal to l(x) less than equal to 3 (b) What are the domain and range of l(1/5x) Enter the exact answer Domain Range
  7. SAVE ME ( MATH)

    function p(t) has a domain of 1 less than or equal to t less than or equal to 12 range of -40 < p less than or equal to 160 Find the domain and range for. Enter the exact answers A) P(1/4t+4) B) -1/10p(2t)+46
  8. Math

    HELP PLEASE!!! I'm having some trouble with this question on my Maths hw. Any help is appreciated:) Identify the domain and range of the function. y=-0.25x^2 1. domain: (-oo, 0] range: (-oo, oo) 2. domain: (-oo, oo) range: (-oo, 0] …
  9. Math

    For nth root functions, I know that if "n" is even, then the domain must be equal or greater than zero. If "n" is odd, then domain will be all set of real numbers. But how do I determine the range of an n-th root function?
  10. Math (Domain and range)

    Evaluate the function f(x)={9x+5, x<0 {9x+6, x>(or equal to)0 Determine its domain and range using interval notation?

More Similar Questions