Question

your answer is incorrect.
the table of ordered pairs ((x, y)) gives an exponential function.
write an equation for the function.

(x)	(y)
(0)	(\frac{1}{4})
(1)	(\frac{1}{2})
(2)	(1)

(y = \frac{1}{2}(2)^x)
try again

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the y-intercept (value when $x=0$), and $b$ is the base.

Step2: Find $a$ using $x=0$

When $x=0$, $y=\frac{1}{4}$. Substitute into $y=ab^x$:
$\frac{1}{4} = ab^0$
Since $b^0=1$, $a=\frac{1}{4}$.

Step3: Find $b$ using another point

Use $x=1, y=\frac{1}{2}$. Substitute $a=\frac{1}{4}$ into $y=ab^x$:
$\frac{1}{2} = \frac{1}{4}b^1$
Solve for $b$: $b = \frac{1/2}{1/4} = 2$

Step4: Verify with other points

Check $x=-1$: $y=\frac{1}{4}(2)^{-1} = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$, which matches.
Check $x=2$: $y=\frac{1}{4}(2)^2 = \frac{1}{4} \times 4 = 1$, which matches.

Answer:

$y = \frac{1}{4}(2)^x$