Question

for an even - degree polynomial with a positive leading coefficient, what is the end behavior?
graph comparison
$y = x^2$: rise right, rise left
end behavior
as $x\to +\infty$, $f(x)\to +\infty$; as $x\to -\infty$, $f(x)\to +\infty$
options:
fall right, fall left
rise right, rise left
rise right, fall left
fall right, rise left

Explanation:

Step1: Recall End Behavior Rules

For a polynomial \( f(x)=a_nx^n + \dots+a_1x + a_0 \), end behavior depends on degree (\( n \)) and leading coefficient (\( a_n \)). For even \( n \) and \( a_n>0 \): as \( x
ightarrow+\infty \), \( x^n
ightarrow+\infty \), so \( f(x)
ightarrow+\infty \) (rise right); as \( x
ightarrow-\infty \), \( (-x)^n=x^n \) (since \( n \) even), so \( f(x)
ightarrow+\infty \) (rise left).

Step2: Match with Options

The option "Rise right, rise left" fits the rule for even - degree polynomial with positive leading coefficient.

Answer:

Rise right, rise left