Question

match each equation with its graph. (do not use technology.)
(a) $y = 5x$
\\(\circ\\) $f$
\\(\circ\\) $f$
\\(\circ\\) $g$
\\(\circ\\) $g$
(b) $y = 5^x$
\\(\circ\\) $f$
\\(\circ\\) $f$
\\(\circ\\) $g$
\\(\circ\\) $g$
(c) $y = x^5$
\\(\circ\\) $f$

Explanation:

Step1: Analyze $y=5x$

This is a linear function with slope $5$, passing through the origin $(0,0)$. It is a straight line, which matches graph $G$.

Step2: Analyze $y=5^x$

This is an exponential function. When $x=0$, $y=5^0=1$, so it passes through $(0,1)$. For $x>0$, it grows rapidly; for $x<0$, it approaches $0$. This matches graph $f$.

Step3: Analyze $y=x^5$

This is an odd-degree polynomial. When $x=0$, $y=0$; when $x=1$, $y=1$; when $x>1$, it grows quickly, and for $x<0$, it is negative. This matches graph $F$.

Answer:

(a) $\boldsymbol{G}$
(b) $\boldsymbol{f}$
(c) $\boldsymbol{F}$