which of the following is the graph of y = e^x + 1?
which of the following is the graph of y = e^x + 1?
Answer
Answer:
The second - graph (from the left)
Explanation:
Step1: Analyze the basic function $y = e^{x}$
The function $y = e^{x}$ has a $y$ - intercept at $(0,1)$ and is an increasing exponential function with a horizontal asymptote at $y = 0$.
Step2: Analyze the function $y=e^{x}+1$
The graph of $y = e^{x}+1$ is a vertical shift of the graph of $y = e^{x}$ upwards by 1 unit. So the $y$ - intercept of $y = e^{x}+1$ is at $(0,2)$ and the horizontal asymptote is at $y = 1$. The first graph has a $y$ - intercept below 2, the second graph has a $y$ - intercept at 2 and is increasing, and the third graph is a decreasing function. So the graph of $y = e^{x}+1$ is the second graph.