Task: Sketch the graph of the function $f(x)=-\sin\left(x+\frac{π}{2}\right)+2$.
Robin sketched the graph of the function $f$ in the following steps (see the figure):
(1) Robin declared that the parent function of the function $f$ is the function $$f_1(x)=\sin x$$ and sketched its graph (in green).
(2) He then determined that the graph of the function $$f_2(x)=\sin\left(x+\frac{\pi}{2}\right)$$ is created by shifting the graph of $f_1$ by $\frac{\pi}{2}$ in the negative direction along the $x$-axis, and he sketched the graph (in blue) of $f_2$.
(3) Robin claimed that the graph of the function $$f_3(x)=-\sin\left(x+\frac{\pi}{2}\right)$$ is symmetric to the graph of $f_2$ across the $y$-axis. Thus, the graph of $f_3$ is identical to the graph of $f_2$.
(4) Finally, he considered the coefficient $2$, which shifts the graph of $f_3$ by $2$ in the positive direction along the $y$-axis. By applying this shift, Robin obtained the resulting graph (in red) of the function $f$.
Robin made a mistake in his procedure. In which step did Robin make a mistake?
The mistake is in step (1). The graph of the function $f_1(x)=\sin x$ does not correspond to the graph of $f_1$ in the figure.
The mistake is in step (2). The graph of the function $f_2(x)=\sin\left(x+\frac{\pi}{2}\right)$ should be created by shifting the graph of $f_1$ by $\frac{\pi}{2}$ in the positive direction along the $x$-axis.
The mistake is in step (3). The graph of $f_3$ should be symmetric to the graph of $f_2$ across the $x$-axis.
The mistake is in step (4). The graph of $f$ should be created by shifting the graph of $f_3$ by $2$ in the negative direction along the $y$-axis.
The graph of $f_3$ should be symmetric to the graph of $f_2$ across the $x$-axis. The next figure shows the correct solution.
