which of the following shows the graph of y = 4^x + 3?

Explanation:

Step1: Analyze the exponential - function properties

The general form of an exponential function is $y = a^x + k$, where $a>0,a\neq1$. For the function $y = 4^x+3$, the base $a = 4>1$, so the function is an increasing exponential function. When $x = 0$, $y=4^0 + 3=1 + 3=4$.

Step2: Check the y - intercept

The y - intercept of the function $y = 4^x+3$ is the value of $y$ when $x = 0$. We found that $y(0)=4$. Also, as $x\to-\infty$, $4^x\to0$ and $y\to3$. The function has a horizontal asymptote at $y = 3$.

Answer:

The graph that has a y - intercept at $(0,4)$ and a horizontal asymptote at $y = 3$ and is an increasing function is the correct graph of $y = 4^x+3$. Without seeing all the options, based on the above - derived properties, the upper - shown graph (assuming the upper graph has a y - intercept at 4 and a horizontal asymptote near $y = 3$ and is increasing) is likely the correct one.