How do you find the domain and range of #y=2/(8x)#?

Question

Hazel Anglin · Accepted Answer

You may as well write #y=1/(4x)# Domain: #x!=0# Range: #y!=0# Both #x=0# and #y=0# are asymptotes. graph{1/(4x) [-10, 10, -5, 5]}

Eva Adamson · Answer

undefined To find the domain and range of the function $y = \frac{2}{8x}$:

1. **Domain**: The domain consists of all allowable input values for $x$ that do not result in division by zero. Since division by zero is undefined, the denominator $8x$ cannot be equal to zero. Therefore, the domain is all real numbers except $x = 0$.

Domain: $x \neq 0$

2. **Range**: To find the range, consider the behavior of the function as $x$ approaches positive and negative infinity. As $x$ approaches positive infinity ($x \rightarrow +\infty$), $8x$ grows without bound, causing $y$ to approach zero. Similarly, as $x$ approaches negative infinity ($x \rightarrow -\infty$), $8x$ also grows without bound, and $y$ approaches zero.

Therefore, the range of the function is all real numbers except $y = 0$.

Range: $y \neq 0$