MHB Find the constants given the domain and range

AI Thread Summary
To find constants B and C for the function y = f(x) with a domain of 1 ≤ x ≤ 6 transformed to 8 ≤ x ≤ 9, B must be positive, allowing for algebraic manipulation to create two equations based on the endpoints. For the second part, to adjust the range of Af(x) + D from −3 ≤ y ≤ 5 to 0 ≤ y ≤ 1, constants A and D can be determined by setting up equations that align the new range with the original. The discussion emphasizes the need for algebraic relationships to solve for the constants effectively. Understanding the composition of functions is crucial for these transformations. The thread highlights the importance of correctly applying function transformations in pre-calculus.
bcast
Messages
1
Reaction score
0
Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 6 and the range of f(x) is −3 ≤ y ≤ 5.

a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9
B=
C=

b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1
A=
D=

I'm working on composition of functions and completely lost at this point.
 
Mathematics news on Phys.org
Hello and welcome to MHB, bcast!

I have moved your topic from the Analysis forum as this is a Pre-calculus topic.

For the first problem, I would begin with the function's new domain:

$$8\le x\le9$$

Now, assuming $B$ is positive, can you algebraically get $B(x-C)$ in the middle, and then equating the end-points to the originals, you will have two equations in two unknowns?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

B Cosecant function: notation for the domain and range -- Am I right?
Replies
6
Views
1K
I Transformation of Functions: How Do Domain and Range Change?
Replies
4
Views
2K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
Replies
2
Views
2K
B Advice to obtain the domain of compound functions
Replies
2
Views
1K
MHB Find Domain & Range of 8 Mathematics Problems for CSE Exam
Replies
1
Views
2K
MHB What Is the Domain and Range of y=cos(3(x - 45°)) +2?
Replies
3
Views
1K
MHB GRE.al.4 Find the domain of \sqrt{x^2-25}
Replies
3
Views
1K
B Finding the range of an equation with domain restrictions?
Replies
2
Views
1K
MHB Find the Range of a Rational Function.
Replies
1
Views
1K
MHB How to Learn Domain,Range and Real Number Of Function Mathematics ?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top