Question

match each equation with its graph. (do not use technology.)
(a) $y = x^2$
\bigcirc $h$
\bigcirc $g$
\bigcirc $f$
(b) $y = x^3$
\bigcirc $f$
\bigcirc $h$
\bigcirc $g$
(c) $y = x^6$
\bigcirc $g$
\bigcirc $h$
\bigcirc $f

Explanation:

Step1: Analyze parity & growth of $y=x^2$

$y=x^2$ is even (symmetric over y-axis). For $0 x^6$; for $x>1$, $x^2 < x^6$. So it is the widest curve on $(0,1)$, matching $h$.

Step2: Analyze parity & shape of $y=x^3$

$y=x^3$ is odd (symmetric about origin), only matches curve $f$.

Step3: Analyze parity & growth of $y=x^6$

$y=x^6$ is even. For $01$, $x^6 > x^2$. So it is the narrowest curve on $(0,1)$, matching $g$.

Answer:

(a) h
(b) f
(c) g