question 1 - 9 which statement describes the end behavior of the function f(x)=-e^{12x}? as x approaches -∞…
question 1 - 9 which statement describes the end behavior of the function f(x)=-e^{12x}? as x approaches -∞, f(x) approaches -∞. as x approaches -∞, f(x) approaches 0. as x approaches -∞, f(x) approaches e. as x approaches -∞, f(x) approaches +∞.
Answer
Explanation:
Step1: Recall exponential - function property
The general form of an exponential function is $y = a\cdot b^{x}$, where $a\neq0$, $b>0$ and $b\neq1$. For the function $y = e^{x}$, as $x\to-\infty$, $e^{x}\to0$.
Step2: Analyze the given function
We have the function $f(x)=-e^{12x}$. Let $u = 12x$. As $x\to-\infty$, $u\to-\infty$. And $y=-e^{u}$. Since as $u\to-\infty$, $e^{u}\to0$, then $y=-e^{u}\to0$ as $u\to-\infty$ (or $x\to-\infty$).
Answer:
As $x$ approaches $-\infty$, $f(x)$ approaches $0$.