Function - one linear, one rational - is the following True or False

In summary, the functions ƒ(x) and g(x) have values of 7 and 5.6 for ƒ(3) and g(3), respectively, and values of 5 and 6.7 for ƒ(4) and g(4), respectively. There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that is closer to 3 than 4. However, it is possible to find examples where x is closer to 4 than 3. Therefore, the statement "There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that
  • #1
bigazonk
2
0
The function ƒ(x) is a linear function and g(x) is a rational function.

These functions have the following values:
ƒ(3) = 7 g(3) = 5.6
ƒ(4) = 5 g(4) = 6.7

There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that must be closer to 3 than 4.

TRUE or FALSE?
 
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  • #2
Hello and welcome to MHB, bigazonk! (Wave)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
  • #3
Certainly there exist x in that interval such that f(x)= g(x) but it is easy to find examples in which x is closer to 4 than to 3.
 

FAQ: Function - one linear, one rational - is the following True or False

What is a linear function?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has a constant rate of change and can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

What is a rational function?

A rational function is a mathematical function that can be written as the ratio of two polynomials. It can have one or more vertical asymptotes and can be written in the form f(x) = (ax + b)/(cx + d), where a, b, c, and d are constants.

What is the difference between a linear function and a rational function?

The main difference between a linear function and a rational function is that a linear function has a constant rate of change and can be represented by a straight line, while a rational function can have a variable rate of change and can have asymptotes.

Is every linear function also a rational function?

Yes, every linear function can also be written as a rational function by setting the denominator of the rational function to 1. For example, the linear function f(x) = 2x + 3 can be written as the rational function f(x) = (2x + 3)/1.

Is every rational function also a linear function?

No, not every rational function is also a linear function. A rational function can only be considered a linear function if the degree of the numerator is equal to the degree of the denominator. If the degrees are not equal, then the function is not linear.

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