In the following graph, write down a possible value of n and the corresponding value of b for the equation.

1. Use the graph shape to decide the type of power function

The graph is a curve which goes down to the left and rises to the right. This is the typical shape of $y=x^n+b$ when $n$ is a positive odd integer, such as $3,5,7,\ldots$.

Since the graph is curved, choose the simplest positive odd exponent greater than $1$: $n=3$.

1. Substitute the point and earlier value of $n$ into the equation

From part (a), $n=3$. Since the curve passes through $(1,-1)$,
$-1=1^3+b$

2. Solve for $b$

$-1=1+b$
$b=-2$