Answer: [tex]2(4)^{x+8}-2[/tex]
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Explanation:
To translate or shift 7 units to the left, we replace x with x+7
So,
[tex]f(x) = 2(4)^{x+1}-2\\\\f(x+7) = 2(4)^{x+7+1}-2\\\\f(x+7) = 2(4)^{x+8}-2\\\\g(x) = 2(4)^{x+8}-2\\\\[/tex]
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Extra info:
If you're wondering "why x+7 and not x-7?" it's because we effectively moved the xy axis 7 units to the right while keeping the f(x) curve fixed in place. This gives the illusion the f(x) curve is moving 7 units to the left.
The graph of each is shown below. I used GeoGebra to make the graph.
