# How do you find the domain and range for y= -2x+3, x>0?

Aug 3, 2015

Domain: $\left(0 , + \infty\right)$
Range: $\left(- \infty , 3\right)$

#### Explanation:

The problem actually gives you the domain of the function as being described by $x > 0$.

More specifically, the domain of the functioncannot include negative values of $x$, as well as $x = 0$.

This means that the domain of the function will be $\left(0 , + \infty\right)$.

Now for the range of the function. SInce $x$ is always positive, the term $- 2 x$ will always be negative. You can find the range of the function by using $x = 0$ to find the maximum value $f \left(x\right)$ cannot take

$f \left(0\right) = - 2 \cdot 0 + 3 = 3$

This means that the function's range will be $\left(- \infty , 3\right)$, since $f \left(x\right)$ will produce a value smaller than $3$ for any $x$ belonging to the $\left(0 , + \infty\right)$ domain.