Answer
Given below.
Work Step by Step
(a)
Since a function $f$ has an inverse that is a function, if there is no horizontal line that intersects the graph of the given function at more than one point.
But, in this case, the horizontal line $y=2$ can be drawn to cut the graph of the function at more than one point. Therefore, the given function fails the horizontal line test, and hence, does not have an inverse that is a function.
(b)
To find the times of day when the average happiness level is 3, draw a line parallel to the horizontal axis, passing through the point 3 on the vertical axis.
Find where this line intersects the given graph and note the corresponding values on the horizontal axis. In this case, this horizontal line cuts the graph at two points, namely $t=12$ and $t=19$.
Thus, the average happiness level was 3 at $12:00\text{ p}\text{.m}\text{.}$ and $10:00\text{ p}\text{.m}\text{.}$ respectively. These values can be represented as $\left( 12,3 \right),\left( 22,3 \right)$.
(c)
No, the function doesn’t represent a one-to-one function because we are able to $x$ which gives the same value of $y$ when given as an input in the function.
Thus, the given function is not one-to-one.
