George was explaining to his classmates what properties the function $f$ has if the graph was given by three line segments.
He explained that:
(1) Every line segment in the figure is part of a line, and every line is the graph of a linear function.
(2) All three lines, which are the extensions of the line segments in the figure, have a positive slope, and therefore they are graphs of increasing linear functions.
(3) The given function $f$ is therefore increasing on the intervals $(-1;2]$, $(5;9)$ and $[9;14]$.
(4) Since the function $f$ is increasing on intervals $(-1;2] $, $(5;9)$, $[ 9;14] $, it is also increasing on the set $(−1;2] \cup (5;9) \cup [ 9;14] $.
Did he make a mistake? If yes, determine where:
Yes, there is a mistake in the part (4). The monotonicity of the function $f$ on individual intervals cannot provide any relevant information about the monotonicity of $f$ on the union of those intervals.
Yes, there is a mistake in the part (4). Since the function $f$ is increasing on intervals $(-1;2]$, $(5;9)$, $[ 9;14]$, it is also increasing on the interval $(-1;14]$.
Yes, there is a mistake in the part (2). The monotonicity of the linear function cannot be determined by the slope of the given straight line.
Yes, there is a mistake in the part (3). Function $f$ can be increasing solely on open intervals.
No. There is no mistake in George’s explanation.
Yes, there is a mistake in the part (1). Only one line segment includes both its endpoints.
