$$ \left\{\begin{array}{l} ext { What is the range of the exponential function } \ g(x)=4^{x}-8 ext { ? }\end{array} ight. $$

Question

$$ \left\{\begin{array}{l}	ext { What is the range of the exponential function } \ g(x)=4^{x}-8 	ext { ? }\end{array}ight. $$

UpStudy AI · Accepted Answer

1. Recall that the basic exponential function $$ f(x) = 4^x $$ has a range of $$ (0, \infty) $$.

2. The given function is $$ g(x) = 4^x - 8 $$. This is a vertical shift downward by 8 units of the function $$ f(x) $$.

3. Shifting the range $$ (0, \infty) $$ downward by 8 units results in the range $$ (0 - 8, \infty - 8) $$, which simplifies to $$ (-8, \infty) $$.

Thus, the range of the function $$ g(x) = 4^x - 8 $$ is $$ (-8, \infty) $$.
The range of $$ g(x) = 4^x - 8 $$ is all real numbers greater than -8.

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