what is the range of $f(x) = (\\frac{3}{4})^x - 4$?\n\\(\\{y|y > - 4\\}\n\\(\\{y|y > \\frac{3}{4}\\}\n\\(\\{y…

what is the range of $f(x) = (\\frac{3}{4})^x - 4$?\n\\(\\{y|y > - 4\\}\n\\(\\{y|y > \\frac{3}{4}\\}\n\\(\\{y|y < - 4\\}\n\\(\\{y|y < \\frac{3}{4}\\})

what is the range of $f(x) = (\\frac{3}{4})^x - 4$?\n\\(\\{y|y > - 4\\}\n\\(\\{y|y > \\frac{3}{4}\\}\n\\(\\{y|y < - 4\\}\n\\(\\{y|y < \\frac{3}{4}\\})

Answer

Explanation:

Step1: Analyze the exponential function

The exponential function $y = (\frac{3}{4})^x$ has the property that for all real - valued $x$, $(\frac{3}{4})^x>0$. This is because the base $\frac{3}{4}\in(0,1)$ and any non - zero number raised to a real power $x$ is positive.

Step2: Find the range of $f(x)$

Let $y = f(x)=(\frac{3}{4})^x - 4$. Since $(\frac{3}{4})^x>0$, then $y=(\frac{3}{4})^x - 4>0 - 4$. So $y>-4$.

Answer:

${y|y > - 4}$