At $x=0$, shouldn't this function be $0$?

Question

function is $f(x)=2.3^{3x\ }-\ 4.3^{2x\ }+2.3^x$ (Dots mean multiply)

according to me, at $x=0$, $f(0)=2\times 1-4 \times 1 + 2\times 1=0$

But why does this graph says otherwise?

Am I having a brain fade or This calculator needs to be abandoned?

Answer 1

Looks like you may have plotted the function incorrectly.

Answer 2

Notice that \begin{align*} f(x) = 2\cdot 3^{3x} - 4\cdot 3^{2x} + 2\cdot 3^{x} & = 2\cdot(3^{x})^{3} - 4\cdot(3^{x})^{2} + 2\cdot 3^{x} = 2\cdot 3^{x}[(3^{x})^{2} - 2\cdot 3^{x} + 1]\\ &= 2\cdot 3^{x}(3^{x}-1)^{2} \end{align*}

Therefore $f(x) = 0$ iff $3^{x} - 1 = 0$, which means you are right.