(a) The graph of a function $y = f(x)$ is shifted to the left $8$ units. Find an equation for this shifted 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 $y = e^x$ is shifted to the left $8$ units. Find an equation for this shifted function.
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(c) The graph of a function $y = g(x)$ is shifted to the right $3$ units. Find an equation for this shifted 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 shifted to the right $3$ units. Find an equation for this shifted function.
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