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

what is the range of $f(x)=\\left(\\frac{3}{4}\\right)^x - 4$?\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 $f(x)=\\left(\\frac{3}{4}\\right)^x - 4$?\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 $y = a^x$ where $0\lt a\lt1$ (here $a=\frac{3}{4}$) has the property that for all real - valued $x$, $a^x>0$. So, $(\frac{3}{4})^x>0$.

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

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

Answer:

${y|y > - 4}$