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

Apr 3, 2018

Ask yourself where the function is defined.

#### Explanation:

In your case the domain is the whole real ax $\mathbb{R}$ and the range too. This is typical for all polynomials.

Other examples:

• logarithmic functions: $f \left(x\right) = \log \left(x\right)$
logarithmic functions are not defined for non positive argument so check where the argument is $\le 0$.

$\log \left(x - 2\right)$ $\Rightarrow$ $x - 2 = 0$ , $x = 2$
$x - 2 \le 0$ , $x \le 2$
$f \left(x\right)$ is defined for $x \le 2$, so the domain is $\left(2 , \infty\right)$
The range is $\mathbb{R}$.

• exponential functions:
$f \left(x\right) = {e}^{x}$
The domain is $\mathbb{R}$ and the range too.

• trigonometric functions:

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

Remember that $\tan \left(x\right)$ has a period $\pi$.
graph{tan(x) [-5, 5, -5, 5]}