# Assignment 1

Common Mistakes:

• To sketch the graph of section 1.1 exercise 16, one really needs to mark the time, one hour, at which the temperature usually gets to its maximum. Few students missed the part before or after the pie is removed from the oven.
• Notice that the domain of a function is simply where the function makes sense. For section 1.1 exercise 38, $g(x)=|x|-x$ always makes sense for any real number $x$.
• On section 1.2 exercise 54, some students made mistakes in subproblem (e) and (f). Please pay attention to how the functions are composited. For instance, $g\circ f(x)$ equals $g(f(x))$, instead of $f(g(x))$.
• A lot of students failed to give a correct answer on section 1.2 exercise 64. According to the question, we know that $g\circ f(x)=h(x)$. On the left hand side, $g\circ f(x)=g(f(x))=g(x+4)$. Thus we have $g(x+4)=h(x)=4x-1$. Now observe that $g(x)=g(x-4+4)=g((x-4)+4)$. Now use $g(x+4)=4x-1$ to get the answer.