Questions: Use transformations of the graph (y=e^x) to graph the function. Write the domain and range in interval notation. (f(x)=e^x+1)

Transcript text: 18 Multiple Choice 1 point Use transformations of the graph $y=e^{x}$ to graph the function. Write the domain and range in interval notation. \[ f(x)=e^{x}+1 \]

Solution

Solution Steps

Step 1: Identify the Base Function

The base function given is $ y = e^x $. This is an exponential function with a horizontal asymptote at $ y = 0 $.

Step 2: Determine the Transformation

The function $ f(x) = e^x + 1 $ is a vertical shift of the base function $ y = e^x $. Specifically, it is shifted 1 unit upwards.

Step 3: Graph the Transformed Function

To graph $ f(x) = e^x + 1 $, take the graph of $ y = e^x $ and shift every point 1 unit upwards. The horizontal asymptote of the graph will also shift from $ y = 0 $ to $ y = 1 $.

Step 4: Determine the Domain

The domain of the function $ f(x) = e^x + 1 $ is the same as the domain of the base function $ y = e^x $, which is all real numbers. In interval notation, this is: \[ (-\infty, \infty) \]

Step 5: Determine the Range

The range of the function $ f(x) = e^x + 1 $ is all values greater than 1, since the graph is shifted 1 unit upwards. In interval notation, this is: \[ (1, \infty) \]

Final Answer

Domain: $\boxed{(-\infty, \infty)}$
Range: $\boxed{(1, \infty)}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!