below is the graph of $y=b^{x}$. find $b$.

Explanation:

Step1: Identify a point on the graph

The graph passes through $(-2, 4)$.

Step2: Substitute point into the function

Substitute $x=-2$, $y=4$ into $y=b^x$: $4 = b^{-2}$

Step3: Rewrite negative exponent

Use $b^{-n}=\frac{1}{b^n}$: $4 = \frac{1}{b^2}$

Step4: Solve for $b^2$

Rearrange to isolate $b^2$: $b^2 = \frac{1}{4}$

Step5: Solve for positive $b$

Since $b>0$ (for exponential function), take square root: $b = \sqrt{\frac{1}{4}} = \frac{1}{2}$

Answer:

$\frac{1}{2}$