which graph represents a reflection of f(x) = 2(0.4)^x across the y - axis?
which graph represents a reflection of f(x) = 2(0.4)^x across the y - axis?
Answer
Explanation:
Step1: Recall reflection rule
The rule for reflecting a function $y = f(x)$ across the $y$-axis is $y=f(-x)$. Given $f(x)=2(0.4)^{x}$, the reflected - function is $g(x)=2(0.4)^{-x}=2\left(\frac{1}{0.4}\right)^{x}=2(2.5)^{x}$.
Step2: Analyze properties of exponential functions
The function $y = a\cdot b^{x}$ where $a = 2$ and $b = 2.5>1$ is an exponential growth function. It has a $y$-intercept of $y(0)=2(2.5)^{0}=2$. As $x$ increases, $y$ increases rapidly.
Answer:
The graph of an exponential growth function with a $y$-intercept of 2.