Find the constants given the domain and range

In summary, for the first problem, the constants B and C can be found by setting up two equations using the new domain of the function, 8 ≤ x ≤ 9, and solving for B and C. For the second problem, the constants A and D can be found by setting up a new range for the function, 0 ≤ y ≤ 1, and solving for A and D.
  • #1
bcast
1
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.
 
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  • #2
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:

\(\displaystyle 8\le x\le9\)

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?
 

FAQ: Find the constants given the domain and range

What is the purpose of finding the constants given the domain and range?

Finding the constants given the domain and range is important because it helps determine the values of a function for specific inputs. This information is useful in graphing and analyzing the behavior of the function.

How do you find the constants given the domain and range?

To find the constants given the domain and range, you need to use the given information to write an equation in the form of y = mx + b. Then, you can use the coordinates of the domain and range to solve for the unknown constants.

Can you find the constants if the domain and range are not given?

No, the constants cannot be found without the domain and range information. The domain and range are essential in determining the behavior of the function and finding the unknown constants.

Are there any specific steps to follow when finding the constants given the domain and range?

Yes, there are specific steps to follow when finding the constants. First, you need to identify the given domain and range and write them in the form of ordered pairs. Then, plug in the values of the ordered pairs into the equation y = mx + b and solve for the unknown constants.

Can finding the constants given the domain and range be used in real-life situations?

Yes, finding the constants given the domain and range can be used in real-life situations, such as in finance and economics. For example, using this method can help determine the cost of production for a company based on its sales and expenses.

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