Now answer the question:
1 answer:
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Answer:
See explanation below for further details.
Step-by-step explanation:
A rational consist of two real numbers such that:
If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.
If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example:
If and
, then:
If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.
Example
If and
, then:
But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.
Example
If and
, then:
Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.
If and
, then:
Example
It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.
Example
Step-by-step explanation:
An exponential function is represented by function,
Where a is the y intercept and b is the growth factor.
The graph passes through (0,1) which is our y intercept so a=1
Know let find b.
The graph pass through (1,3) so plug in 1 for x and 3 for y.
So our base function is
In order for this function to shrink, we must shift the y intercept such that it is less than 1 but greater than -1.
So the only option is
Because 1/2<1