Answer
a) no; b) yes; c) no; d) no; e) yes
Work Step by Step
a) $f(x)=3x+1$
$y=3x+1$
The intercepts are:
$y=0\Rightarrow 3x+1=0\Rightarrow x=-\dfrac{1}{3}$
$x=0\Rightarrow y=3(0)+1=1$
The function does not fit because the $x$-intercept of the function $f$ is negative.
b) $g(x)=-2x+3$
$y=-2x+3$
The intercepts are:
$y=0\Rightarrow -2x+3=0\Rightarrow x=1.5$
$x=0\Rightarrow y=-2(0)+3=3$
The $x$-intercept is positive; the $y$-intercept is positive and its graph has negative slope, so $g$ fits.
c) $H(x)=3$
The function does not fit because its graph is a horizontal line.
d) $F(x)=-4x-1$
$y=-4x-1$
The intercepts are:
$y=0\Rightarrow -4x-1=0\Rightarrow x=-0.25$
$x=0\Rightarrow y=-4(0)-1=-1$
The intercepts are negative; therefore $F$ doesn't fit.
e) $G(x)=-\dfrac{2}{3}x+3$
$y=-\dfrac{2}{3}x+3$
The intercepts are:
$y=0\Rightarrow -\dfrac{2}{3}x+3=0\Rightarrow x=4.5$
$x=0\Rightarrow y=-\dfrac{2}{3}(0)+3=3$
The $x$-intercept is positive. The $y$-intercept is positive, and its graph has negative slope; therefore $G$ fits.
