Don't laugh. Make a graph! When you are trying to find domain, it's best to graph it and look at the x and values.
The domain is (0,∞). Notice that left to right the function never quite touches the x value of 0. As you look right, it will go forever. Also notice there is a vertical asymptote at x = 0. The range is all real numbers.
Example 2
What is the range of f(x) = log10x?
Same graph! Range is the possible y values of a function. Look down at the bottom of the function. How low are we looking? Look up towards the top of the function. Does it keep going forever? Whatever direction it goes forever, we say infinity or ∞. Now go get that tattooed on your ankle: ∞.
The domain is (0,∞). Notice that left to right the function never quite touches the x value of 0. As you look right, it will go forever. Also notice there is a vertical asymptote at x = 0. The range is all real numbers.
Example 3
Graph f(x) = log2x.
On our nifty graphing calculator, try putting this in for your equation: . Don't have a graphing calculator? If you are reading this, that means you are on the Internet. Go look for an online graphing calculator or use our Best of the Web links to find ones we suggest.
. Don't have a graphing calculator? If you are reading this, that means you are on the Internet. Go look for an online graphing calculator or use our Best of the Web links to find ones we suggest.