Question

complete parts a. and b. below.
b. graph the function $y = x^3 + 1$ with a graphing calculator using the viewing window $x_{\text{min}} = -4$, $x_{\text{max}} = 4$, $y_{\text{min}} = -35$, $y_{\text{max}} = 35$. choose the correct graph below.
\bigcirc a.\bigcirc b.\bigcirc c.\bigcirc d.

Explanation:

1. First, identify key features of $y=x^3+1$: it is a cubic function, increasing everywhere, with a y-intercept at $(0,1)$ (when $x=0$, $y=0^3+1=1$) and x-intercept at $(-1,0)$ (when $y=0$, $x^3+1=0 \Rightarrow x=-1$).
2. Eliminate options C and D, as they show decreasing functions (matching $y=-x^3$ type, not $y=x^3+1$).
3. Compare A and B: check the behavior near $x=0$. The function $y=x^3+1$ has a value of 1 at $x=0$, so the graph should pass above the x-axis at $x=0$. Option B matches this, while Option A appears to flatten near $y=0$ at $x=0$, which is incorrect. The provided full graph also confirms the shape matches Option B.

Answer:

B. <The graph of an increasing cubic function passing through (-1,0) and (0,1), curving upward for positive x and downward for negative x>