Question

How do you find the domain and range of `y=2x^2 - 4x - 5`?

Answer 1

Ask yourself where the function is defined.

Explanation:

In your case the domain is the whole real ax `RR` and the range too. This is typical for all polynomials.

Other examples:

• logarithmic functions: `f(x)=log(x)`
  logarithmic functions are not defined for non positive argument so check where the argument is `<=0`.

`log(x-2)` `rArr` `x-2=0` , `x=2`
`x-2<=0` , `x<=2`
`f(x)` is defined for `x<=2`, so the domain is `(2, infty)`
The range is `RR`.

• exponential functions:
  `f(x)=e^x`
  The domain is `RR` and the range too.
  

• trigonometric functions:

  • `sin(x), cos(x)`: The domain is `RR`, the range `[-1,1]`
    
  • `tan(x)` The domain is `RR-{k pi/2}; k in ZZ`, the range is `RR`
    Look at the unit circle, the distance between the x-ax and the intersection of the green and blue line is `tan(x)`, where `x` is the angle. If `x rarr pi/2` there is no intersection of the green and blue line, there `tan(x)` is not defined.

Remember that `tan(x)` has a period `pi`.
graph{tan(x) [-5, 5, -5, 5]}