Let f(x) represents the heart beat of the person.
Now, we have been given that person’s theoretical maximum heart rate is given by 220 - x.
Also, we have been given that person strive for a heart rate that is at least 50% of the maximum. At least means greater than equal to.
Thus, we have
Also, we have been given that person strive for a heart rate that is at most 75% of the maximum. At most means less than equal to.
Therefore, the system of inequality is given by
Answer:
Domain [-5,∞)
Range [0,∞)
Step-by-step explanation:
Part 1) Find the domain
we have
we know that
The radicand must be greater than or equal to zero
so
solve for x
subtract 5 both sides
The solution for x is the interval [-5,∞)
All real numbers greater than or equal to -5
Remember that
The domain of a function is the set of all possible values of x
therefore
The domain of the function f(x) is the interval [-5,∞)
Part 2) Find the range
we have
Find the value of f(x) for the minimum value of x
For x=-5
The minimum value of f(x) is equal to zero
so
The solution for f(x) is the interval [0,∞)
All real numbers greater than or equal to 0
Remember that
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
therefore
The range of the function is the interval [0,∞)