(a) The graph of a function $y = f(x)$ is horizontally compressed by a factor of $2$ and reflected about the $y$-axis. Find an equation for this compressed and reflected function in terms of the function $f(x).$ For example, $y = 10 f(9x+8) + 7.$
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(b) The graph of the function $y = e^x + 10$ is horizontally compressed by a factor of $2$ and reflected about the $y$-axis. Find an equation for this compressed and reflected function.
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(c) The graph of a function $y = g(x)$ is horizontally expanded by a factor of $7$ and reflected about the $x$-axis. Find an equation for this expanded and reflected function in terms of the function $g(x).$ For example, $y = 10 g(9x+8) + 7.$
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(d) The graph of the function $y = x^3 - 2x$ is horizontally expanded by a factor of $7$ and reflected about the $x$-axis. Find an equation for this expanded and reflected function.
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