Evaluate the function
f(x)={9x+5, x<0
{9x+6, x>(or equal to)0
Determine its domain and range using interval notation?
I believe the domain is (-infinity,infinity) but how would I find the range?
also -oo to +oo
the interval (5,6] is excluded from the range, because of the jump at x=0.
To find the domain and range of a function, we need to consider the possible values for the input (x) and the corresponding output (f(x)). In this case, we have two different expressions for f(x) depending on the value of x.
Let's first determine the domain of the function:
For the given function f(x) = {9x+5, x<0} and {9x+6, x≥0}, the domain includes all possible values of x for which the function is defined.
In this case, there are no restrictions on the values of x, as the expressions 9x+5 and 9x+6 are defined for all real numbers. Therefore, the domain of the function is (-∞, ∞), which means all real numbers.
Now let's find the range of the function:
To determine the range, we need to consider the possible values of f(x) for all valid x values.
For f(x) = 9x+5, where x<0:
As x<0, the expression 9x+5 can be any real number greater than or equal to 5. So, the range for this part of the function is [5, ∞).
For f(x) = 9x+6, where x≥0:
As x≥0, the expression 9x+6 can be any real number greater than or equal to 6. So, the range for this part of the function is [6, ∞).
Combining both ranges, the overall range of the function can be represented as [5, ∞).
Therefore, the domain of the function is (-∞, ∞) and the range is [5, ∞).