Questions: Use the function below to answer the following questions. m(x)=-e^x-1 (a) Use transformations of the graph of y=e^x to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.

Use the function below to answer the following questions.
m(x)=-e^x-1
(a) Use transformations of the graph of y=e^x to graph the given function.
(b) Write the domain and range in interval notation.
(c) Write an equation of the asymptote.

Transcript text: Use the function below to answer the following questions. \[ m(x)=-e^{x}-1 \] (a) Use transformations of the graph of $y=e^{x}$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.

Solution

Solution Steps

Step 1: Reflection across the x-axis

The negative sign in front of the exponential function reflects the graph of $y = e^x$ across the x-axis, resulting in $y=-e^x$.

Step 2: Reflection across the y-axis

The negative sign in the exponent reflects the graph of $y = -e^x$ across the y-axis, resulting in $y = -e^{-x}$.

Step 3: Vertical translation

The subtraction of 1 shifts the graph of $y = -e^{-x}$ downward by 1 unit, giving the final graph of $m(x) = -e^{-x} - 1$.

Final Answer:

The graph of $m(x) = -e^{-x} - 1$ can be obtained from the graph of $y = e^x$ by reflecting it across the x-axis, reflecting it across the y-axis, and then shifting it down by 1 unit.

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