Question

The graph below represents which of the following functions?

Answer 1

This is a more difficult one to explain. Let's start with the line to the right.  It has a slope (m) of $\frac{-2}{2}$ = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2.  The only option that has that equation is A.

Answer: A

Answer 2

First of all, you can see that this is a piecewise polynomial, since it is shaped like a parabola before $x = 2$, and is a line after $x = 2$ So, option C is surely wrong, because it uses $x = 3$ as splitting point.

Moreover, the way the parabola "bounces" on the x axis, avoiding its negative part, tells us that there is an absolute value. This excludes options B and D, and the answer is thus A.