Domain:

\(y\) is a shifted exponential function, therefore its natural domain is \((-\infty , \infty )\).

Continuity:

\(y\) is a shifted exponential function, therefore it is continuous on its domain and has no discontinuities.

\(y\) is a shifted exponential function, therefore it has no singularities.

End-Behavior:

\(y\) is a shifted exponential function. The leading coefficient is \(1\), which is positive. The base is \(\frac {4}{3}\), which is greater than \(1\).

\(\blacktriangleright \) As \(x\) becomes big and negative, then the exponent becomes big and negative. We have a number greater than \(1\) raised to big negative numbers. That will approach \(0\) and then we subtract \(3\)

\(\blacktriangleright \) As \(x\) becomes big and positive, then the exponent becomes big and positive. We have a number greater than \(1\) raised to big positive numbers. That becomes unbounded positively.

Behavior:

\(y\) is a shifted exponential function. The leading coefficient is \(1\), which is positive. The base is \(\frac {4}{3}\), which is greater than \(1\). Therefore, \(y\) is an increasing function.

Shifted exponential functions have no global or local maximums or minimums.

Exponential functions are either increasing or decreasing and since the end-behavior is \(-3\) to \(\infty \), we have that \(y\) is an increasing function.

Zeros:

Since we have a continuous exponential function with negative and positive values, it will have a single zero.

The zero will occur when

\(x\) is the thing you raise \(\frac {4}{3}\) to, to get \(3\).

This all agrees with the graph.