1) Find three functions with unlimited domains and ranges.
2) Find two functions with restricted domains.
3) Find two functions with restricted ranges.
Im confused as to how I can find the answer for these question, can you please explain along the steps.
Sure! I'll explain how you can find the answers to each of these questions step by step:
1) To find three functions with unlimited domains and ranges, you need to understand what it means for a function to have an unlimited domain and range.
A function has an unlimited domain if it can accept any input value. In other words, there are no restrictions on the set of possible inputs for the function. For example, the function f(x) = x is a function with an unlimited domain because it can accept any real number as its input.
Similarly, a function has an unlimited range if it can output any possible value. In other words, there are no restrictions on the set of possible outputs for the function. For example, the function g(x) = 2x is a function with an unlimited range because it can output any real number.
With that understanding, you can find three functions with unlimited domains and ranges by considering functions that can accept and output any real number. For example:
- f(x) = x (identity function)
- g(x) = 2x
- h(x) = sqrt(x)
2) To find two functions with restricted domains, you need to think about functions that have limitations on their input values.
A function with a restricted domain can only accept certain values as inputs. For example, consider the function f(x) = 1/x. This function has a restricted domain because it is undefined when x = 0. So, the domain of this function is all real numbers except 0.
Here are two examples of functions with restricted domains:
- g(x) = sqrt(x) (the square root function has a restricted domain of x ≥ 0)
- h(x) = 1/(x-5) (this function has a restricted domain of all real numbers except x = 5)
3) To find two functions with restricted ranges, you need to look for functions that have limitations on their output values.
A function with a restricted range can only output certain values. For example, consider the function f(x) = x^2. This function has a restricted range because it can only output non-negative values. So, the range of this function is all real numbers greater than or equal to 0.
Here are two examples of functions with restricted ranges:
- g(x) = sin(x) (the sine function has a restricted range of -1 ≤ y ≤ 1)
- h(x) = e^x (the exponential function has a restricted range of y > 0)
I hope this explanation helps you understand how to find functions with both unlimited and restricted domains and ranges!