Question

$f(x) = 0.4^{x}$ and $g(x) = 0.2^{x}$
a. $f(x)$
b. $g(x)$
a
b

Explanation:

Step1: Analyze exponential function behavior

For exponential functions $h(x)=a^x$ where $0

Step2: Compare decay rates

Since $0.2 < 0.4$, $g(x)=0.2^x$ decays faster than $f(x)=0.4^x$. For negative $x$ (left side of the y-axis), $g(x)=0.2^x = (5)^{-x}$ and $f(x)=0.4^x=(2.5)^{-x}$, so $g(x)$ will have larger y-values than $f(x)$ when $x<0$.

Step3: Match to graphs

Graph A is higher (larger y-values) on the left and drops faster, so it corresponds to $g(x)$. Graph B is lower on the left and drops slower, so it corresponds to $f(x)$.

Answer:

a. $f(x)$: B
b. $g(x)$: A