Science:Math Exam Resources/Courses/MATH104/December 2016/Question 09 (c)/Solution 1

From the part (a), we have $a=b=1$.

On the interval $(-\infty ,0]$, we draw the exponential function graph $y=e^{x}$ which ends at the point $(0,1)$.

Then, we can easily draw the linear function $y=x+1$ on the interval $(0,1]$, which starts from the point $(0,1)$ and has the slope $1$ . Indeed, it ends at $(1,2)$.

Finally, on $[2,\infty )$, we draw the graph of $y=1+{\sqrt {x}}$ which can be obtained by translating the graph of $y={\sqrt {x}}$ up 1 unit.

To sum, we get the following sketch of the graph of $y=f(x)$ as follows.