1. The problem is to plot the graph of the highest integer step function, also known as the ceiling function. 2. The ceiling function, denoted as $y=\lceil x \rceil$, maps any real number $x$ to the smallest integer greater than or equal to $x$. 3. This function steps up at every integer value, making it a step function with jumps at integers. 4. The graph is a stepwise constant function that increases by 1 at each integer point. 5. Mathematically, for any $x \in [n, n+1)$ where $n$ is an integer, $y=\lceil x \rceil = n+1$. 6. This means the graph consists of horizontal line segments on intervals $[n, n+1)$ at height $n+1$, with open circles at the left ends and closed circles at the right ends of each segment. 7. The function is defined for all real numbers and has no extrema, as it jumps vertically at integers. Final answer: The ceiling function is $y=\lceil x \rceil$, a step function consisting of step jumps at integers upward by 1.