Question

this is the graph of an exponential function.
write an equation for the function in the form $f(x)=a(b)^x$.
use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$.
$f(x) = $

Explanation:

Step1: Identify y-intercept (a)

The graph crosses the y-axis at $(0, -1)$. For $f(x)=a(b)^x$, when $x=0$, $f(0)=a$. So $a=-1$.

Step2: Find a second point to solve for b

Use the point $(1, -3)$. Substitute $x=1$, $f(1)=-3$, $a=-1$ into the function:
$-1 \cdot b^1 = -3$
Solve for $b$: $b = \frac{-3}{-1} = 3$

Step3: Verify with another point

Check $(2, -9)$: $f(2)=-1 \cdot 3^2 = -9$, which matches the graph.

Answer:

$f(x) = -1(3)^x$ or $f(x) = -(3)^x$