Finding Range of f(x) = (2x - 3) / (x - 2): Help Needed

In summary, the Core 3 way of finding the range of f(x) = (2x - 3) / (x - 2) is to first determine that x cannot be 2, and then use the equation t = (2x - 3) / (x - 2) to find the values of x that correspond to any given t. We also see that the range of the function is all real numbers except 2, and that 2 is a horizontal asymptote for the function.
  • #1
CathyLou
173
1
Hi.

Could someone please tell me the Core 3 way of finding the range of f(x) = (2x - 3) / (x - 2).

I have no idea how to draw the graph.

Any help would be really appreciated.

Thank you.

Cathy
 
Physics news on Phys.org
  • #2
Well, you know that x can't be 2, right?

Now, let "t" denote some arbitrary real number; we are to find out what x must be in order for f to eqal f:
[tex]t=\frac{2x-3}{x-2}\to(x-2)t=2x-3\to{x}=\frac{2t-3}{t-2}, x\neq{2}[/tex]
Thus, t=2 is an inadmissible value for the function.

Note that t=2 is a horizontal ASYMPTOTE for f(x) as x trundles off to either infinity.

Furthermore, there are no t-value such that [tex]\frac{2t-3}{t-2}=2[/tex], whereupon we have shown that the range of f is all real numbers except 2.
 
Last edited:

Related to Finding Range of f(x) = (2x - 3) / (x - 2): Help Needed

1. What is the domain of this function?

The domain of this function is all real numbers except x = 2. This is because the function is undefined at x = 2, as it would result in division by 0.

2. How can I find the range of this function?

To find the range of a function, you can either graph the function and identify the highest and lowest points, or you can use algebraic techniques such as finding the vertical asymptotes and the end behavior of the function.

3. What is the significance of the vertical asymptote in this function?

The vertical asymptote at x = 2 indicates that the function is undefined at this point. It also helps identify the behavior of the function as x approaches 2 from either side.

4. Can I simplify this function further?

Yes, you can simplify this function by factoring the numerator and canceling out common factors with the denominator. In this case, the function can be simplified to f(x) = 2.

5. How can I use this function to solve real-world problems?

This function can be used to solve problems involving rates of change, such as finding the average speed of a moving object or determining the rate of change in a chemical reaction. It can also be used to analyze data sets and make predictions based on the trend of the function.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
896
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
487
  • Calculus and Beyond Homework Help
Replies
25
Views
485
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
772
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
600
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
Back
Top