Question

This graph shows an exponential function.
graph shows two points (0,-2) (1,-3)
Write an equation for the function in the form f(x)=a(b)x.
f(x)=

Answer 1

To find the equation of the exponential function in the form \( f(x) = a(b)^x \), we need to determine the values of \( a \) and \( b \) using the given points \((0, -2)\) and \((1, -3)\).

1. **Using the point \((0, -2)\)**:
\[
f(0) = a(b)^0 = a \cdot 1 = a
\]
Therefore, we have:
\[
a = -2
\]

2. **Using the point \((1, -3)\)**:
\[
f(1) = a(b)^1 = a \cdot b
\]
Plugging in the values, we get:
\[
-3 = -2b
\]
Solving for \( b \):
\[
-3 = -2b \implies b = \frac{-3}{-2} = \frac{3}{2}
\]

Now we can write the equation of the exponential function:
\[
f(x) = -2\left(\frac{3}{2}\right)^x
\]

Thus, the equation is:
\[
f(x) = -2\left(\frac{3}{2}\right)^x
\]