Subjects algebra

Exponential Shift Edce36

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1. The problem asks to describe the transformations to obtain the graph of $g(x) = 8^{x+3}$ from the graph of $f(x) = 8^x$. 2. The general form for horizontal shifts in exponential functions is $f(x + h)$ shifts the graph of $f(x)$ horizontally by $h$ units. 3. If $h$ is positive, the graph shifts to the left by $h$ units; if $h$ is negative, it shifts to the right by $|h|$ units. 4. Here, $g(x) = 8^{x+3}$ means $h = 3$, so the graph of $f$ is shifted 3 units to the left. 5. There is no vertical shift or reflection or stretching involved since the base and coefficient remain unchanged. 6. Therefore, the correct choice is B: The graph of $g$ is the graph of $f$ shifted 3 units to the left. Final answer: The graph of $g$ is the graph of $f$ shifted 3 unit(s) to the left.