ok so i havent done domain and ranges for a while so i need some help this is just a generic question but i want to make sure i know how to do them before starting calc so can someone please explain how i would heres a function f( t) = t+ 3 /(t2 – 5t – 66),
Division is not allowed by zero. So the domain (for t here) cannot include when t is a root of t^2-5t-66=0
http://www.freemathhelp.com/domain-range.html
To find the domain and range of a function, you need to consider the limitations imposed by the function itself. Let's go step by step:
Domain:
The domain of a function refers to the set of all possible input values (or values of the independent variable) for which the function is defined. In other words, we need to determine any restrictions on the variable "t" that would make the function undefined.
In this case, the function is a rational function, as it involves a division operation. We need to ensure that the denominator, t^2 – 5t – 66, is not equal to zero.
To find the values of "t" where the denominator is zero, set t^2 – 5t – 66 = 0 and solve for "t". This quadratic equation can be factored as (t – 11)(t + 6) = 0. So, t = 11 or t = -6.
Therefore, the domain of the function f(t) = t + 3/(t^2 – 5t – 66) is all real numbers except t = 11 and t = -6.
Range:
The range of a function refers to the set of all possible output values (or values of the dependent variable) that the function can produce. To determine the range, we need to analyze the behavior of the function as t approaches positive infinity and negative infinity.
As t approaches positive or negative infinity, the value of f(t) will also approach a certain value. In this case, t + 3/(t^2 – 5t – 66) is dominated by the term t, as the degree of t^2 is higher. Therefore, the range is all real numbers.
To summarize:
Domain: All real numbers, except t = 11 and t = -6.
Range: All real numbers.
It is always a good idea to graph the function and verify these results if possible.