Please use graphs and explain steps well. Thank you!

Question

Please use graphs and explain steps well. Thank you!

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The graph of  is shown below. Assume the domain of  is  and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines.

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

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  and  are on the graph of $y = f\left( 2x - 8 \right).$ Find  and

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.