fill in the blanks so that the resulting statement is true. the graph of f(x)=x³ ______ to the left and…

fill in the blanks so that the resulting statement is true. the graph of f(x)=x³ ______ to the left and ______ to the right. the graph of f(x)=x³ to the left and to the right.

fill in the blanks so that the resulting statement is true. the graph of f(x)=x³ ______ to the left and ______ to the right. the graph of f(x)=x³ to the left and to the right.

Answer

Explanation:

Step1: Analyze the end - behavior of $y = x^3$

The function $y = f(x)=x^3$ is a cubic function with a positive leading coefficient ($a = 1$ in $y=ax^3+bx^2+cx + d$, here $b = c = d=0$).

Step2: Determine left - hand behavior

As $x\to-\infty$, we have $y=x^3\to-\infty$. So the graph falls to the left.

Step3: Determine right - hand behavior

As $x\to+\infty$, we have $y=x^3\to+\infty$. So the graph rises to the right.

Answer:

falls; rises