Question

algebra ii b - spring
$f(x) = -1.5^{x}$ and $g(x) = -2.7^{x}$
a:
b:
a. $f(x)$
b. $g(x)$

Explanation:

Step1: Analyze exponential base growth

For exponential functions of the form $h(x) = -b^x$, the magnitude of the base $b$ determines how quickly the function grows in the negative direction (for $x<0$) and positive direction (for $x>0$). A larger base means faster growth.

Step2: Compare function values at $x=2$

Calculate $f(2) = -1.5^2 = -2.25$
Calculate $g(2) = -2.7^2 = -7.29$
At $x=2$, the value of $g(x)$ is more negative (farther from the x-axis) than $f(x)$. On the graph, curve A is farther from the x-axis at $x=2$, while curve B is closer.

Step3: Match curves to functions

Since $g(x)$ has a larger base and grows faster, it corresponds to curve A. $f(x)$ with the smaller base corresponds to curve B.

Answer:

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