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Concept

$y=a⋅b_{x}$

If the coefficient $a$ is $0,$ the function becomes a horizontal line.
*not* exponential.

$y=0⋅b_{x}⇒y=0 $

This is a line along the $x-$axis and, therefore, is a linear relation. This means that if $a=0,$ then the function is If the base $b$ is negative, the function gives undefined results for certain $x-$values. For example, since $b_{1/2}=b ,$ a negative value for $b$ would yield non-real values for $x=21 .$ Hence, a condition on $b$ is needed.

$b≥0 $

However, if $b=0$ or $b=1$, the function becomes a horizontal line.
$y=a⋅0_{x}⇓y=0 and y=a⋅1_{x}⇓y=a $

Therefore, $b$ cannot be equal to $0$ nor $1.$
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