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The graph of $y = f(x)$ is shown below. Assume the domain of $f$ is $[-4,4]$ and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines.

Part (a): The points $(a,4)$ and $(b,-4)$ are on the graph of $y = f\left( 2x \right).$ Find $a$ and $b.$

Part (b): Find the graph of $y = f\left( 2x \right).$ Verify that your points from part (a) are on the graph.

Part (c): The points $(c,4)$ and $(d,-4)$ are on the graph of $y = f\left( 2x - 8 \right).$ Find $c$ and $d.$

Part (d): Find the graph of $y = f\left( 2x - 8 \right).$ Be sure to verify that your points from part (c) are on the graph both algebraically and geometrically.