Question

what is the domain of the graph of y=log3*x+2

Answer 1

The logarithmic function is not defined for any values of x that are negative. This is because regardless of what exponent you raise a base to, the resulting value will never be negative. Examining this particular function, we can see that it is vertically shifted by 2, but there is not horizontal shift, so the domain is still the set of positive real numbers. This is written as \[(0,\infty)\]or in set builder notation\[\left\{ x \in \mathbb{R}:x >0 \right\}\]