Given: 1.1(3)^x
Just because I prefer it this way write as y=11/10xx3^x
color(blue)("Determine the "y_("intercept"))
The y_("intercept") occurs at x=0
However, 3^0=1 giving
color(brown)(y_("intercept")=11/10xx1 = 11/10)
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color(blue)("Consider the case "x<0)
This changes 3^x into some root of 3
So as x becomes increasingly negative 3^x becomes less and less. So as x tends to negative infinity then:
color(brown)(y=11/10xxlim_(x->oo^(-))(3^x)color(white)("ddd") ->color(white)("ddd")y=11/10xx0=0)
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color(blue)("Consider the case "x>0)
As x becomes increasingly greater the 3^x increases exponentially.
color(brown)(y=11/10xxlim_(x->oo^(+))(3^x)color(white)("ddd") ->color(white)("ddd") y=11/10xxoo = oo
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