Kamila P. answered • 07/10/23
Columbia Engineering Grad with 10+ Years of Math Teaching Experience
Assuming the equation given is y=4t2+5, therefore, in function notation (read as "f of t") it is f(t)=4t2+5.
The domain is all the possible inputs, or independent values, of a function. In this problem, the domain is all the values of the independent variable, t.
The range is all the possible outputs, or dependent values, of a function. Here, the range is all the values of the dependent variable, y.
Since the domain is given as a set of values, in order to find the range, you must evaluate the function for each of these inputs (t-values) in order to find the corresponding outputs (y-values):
f(x) = 4t2+5
f(-3) = 4(-3)2+5 = 41
f(-1.5) = 4(-1.5)2+5 = 14
f(0) = 4(0)2+5 = 5
f(1) = 4(1)2+5 = 9
f(4) = 4(4)2+5 = 69
Therefore, the range corresponding to the given domain is R = {41, 14, 5, 9, 69}
Writing these values in order, you have R = {5, 9, 14, 41, 69}.
