y axis intercept occurs when x=0x=0
y=(1/4)^(0+4)-3=1/256-3=color(blue)(-767/256)y=(14)0+4−3=1256−3=−767256
x axis intercept occurs when y=0y=0
(1/4)^(x+4)-3=0(14)x+4−3=0
(1/4)^(x+4)=3(14)x+4=3
(x+4)ln(1/4)=ln3=>x=(ln3)/(ln(1/4))-4~~color(blue)(-4.792)(x+4)ln(14)=ln3⇒x=ln3ln(14)−4≈−4.792
There are no constraints on xx so domain is:
color(blue)({x in RR})
as x->oo , color(white)(888)(1/4)^(x+4)->0
So:
as x->oo , color(white)(888)(1/4)^(x+4)-3->-3
The line color(blue)(y=-3) color(white)(88) is a horizontal asymptote.
For x<-4
(1/4)^(x+4) becomes color(white)(888)1/((1/4)^(x+4))
So:
as x->-oo , color(white)(888)1/((1/4)^(x+4))->oo
and:
x->-oo , color(white)(888)1/((1/4)^(x+4))-3->oo
Range:
color(blue)({y in RR : -3 < y < oo })
Graph:
![enter image source here]()
