# 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 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. 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

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

posted by Alana K
3. never mind, ignore my last comment, it's incorrect. thank you for your help.

posted by Alana K

## Similar Questions

1. ### math

So for this question it says, the graph of the function f(x)= radical of x+4 is shown. The domain of the function is 1) {x|x is greater than 0} 2) {x|x is greater or equal to 0} 3) {x|x is greater than -4} 4) {x|x is greater than
2. ### Algebra

22. State the domain of the function y=3x+2 a. D: Real numbers b. D: x not equal to 0 c. D: x < 0 A? 23. State the range of the function y=2x^2 a. R: y greater than or equal to 0 b. R: x not equal to 0 c. R: y < 0 I'm not
3. ### 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).
4. ### 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
5. ### math 116

What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a
6. ### college algebra

1.for the given function f&g, find the following and state the domain of each result. f(x)=2x+1/9x-5; g(x) 4x/9x-5 a.(f+g)(x)=? What is the domain? b. (f/g)(x)=? what is the domain? 2.the function f is defined as follows {x+6 if
7. ### college trig

I need to find the domain of the following function: y=arcsin((x-3)/(2x+1)) My math is a bit rusty after holidays...This is what I did: (I'll use <> for the sign of 'not equal') -> 2x+1<>0 <=> 2x<>-1
8. ### Calculous

the figure shows the graph of F', the derivative of a function f. the domain of the function f is the set of all X such that -3< or equal to x<or equal to 3 a)for what values of x in the domain does f have a relative max and
9. ### Precalculus

let the function g be defined by g(x)=1-5x if the domain of the function of g is {x-3 is less than or equal to x which is less than or equal to 2} what is the smallest value of the range show work please
10. ### 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? (more preferably range...I'm okay but shaky on domain) Ex: f(x)=1/(x^2) Also, how do you write the domain

More Similar Questions