evaluate y = e^x + 1 for the following values of x. round to the nearest thousandth. x = -2, y ≈ 1.135 x =…
evaluate y = e^x + 1 for the following values of x. round to the nearest thousandth. x = -2, y ≈ 1.135 x = 1, y ≈ 3.718 x = 2, y ≈ 8.389 complete which of the following is the graph of y = e^x + 1?
Answer
Explanation:
Step1: Analyze key - points of the function
The function $y = e^{x}+1$ is an exponential function $y = e^{x}$ shifted up by 1 unit. The exponential function $y = e^{x}$ has a $y$ - intercept at $(0, 1)$ and passes through the points $(- 1,\frac{1}{e})\approx( - 1,0.368)$ and $(1,e)\approx(1,2.718)$. For $y = e^{x}+1$, the $y$ - intercept is at $(0,2)$ (since when $x = 0$, $y=e^{0}+1=1 + 1=2$), when $x=-1$, $y=\frac{1}{e}+1\approx0.368 + 1=1.368$, and when $x = 1$, $y=e + 1\approx2.718+1 = 3.718$. The function $y = e^{x}+1$ is an increasing function for all real - valued $x$ because the derivative of $y = e^{x}+1$ is $y'=e^{x}>0$ for all $x\in R$.
Step2: Match with the graphs
The first graph has a $y$ - intercept at $(0,2)$ and is an increasing function. The second graph has a $y$ - intercept below 2. The third graph is a decreasing function.