You may have mixed up the graphs for $\displaystyle{f{{\left({x}\right)}}}={{e}}^{{x}}\usepackage{cmbright}\Huge\$ and $\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}\usepackage{cmbright}\Huge\$ . When $\displaystyle{x}={0},\usepackage{cmbright}\Huge\$ the value of the function is $\displaystyle{{e}}^{{0}}={1}.\usepackage{cmbright}\Huge\$ So the point $\displaystyle{\left({0},{1}\right)}\usepackage{cmbright}\Huge\$ is on the graph. Therefore, the graph does cross the y-axis.