Secondary Level Math Questions.
Name : Beth

Find Domain and Range and Zeros:

1. f(x)=15-2x-x²

2. g(t)=square root of 4-t²

3. y=t-3/t²-t-6

Find a rule for h^-1(x) . Then show h(x) and h^-1(x) are inverses. h(x) = x³-1/2

What makes a graph symmetric?
to the origin?
to the y-axis?
to the x-axis?

This looks like a homework assignment so I am not going to do it for you but I will give you a couple of suggestions. I find it sometimes helps to think of functions as machines. You give the machine some input (a number) and the machine does something with the number and then outputs something (again a number). The domain is the collection of valid inputs and the range is the collection of all outputs.

For your second problem the function involves a square root and only non-negative numbers are valid inputs for the square root function. Thus to find the domain for the second problem you need to find all t so that 4-t² is larger than or equal to zero. On the other hand any number is a valid input for the first problem.

To find the range of problem 1 I would plot its graph. For the range of problem 2 the important fact is that the output from the square root function is always non-negative.