Chapter 5: Q. 97 (page 285)

In Problems $97 - 100$ , graph each function. Based on the graph, state the domain and the range and find any intercepts.
$f (x) = \{\begin{cases} e^{- x} i f x < 0 \\ e^{x} i f x \geq 0 \end{cases}$

Short Answer

Expert verified

The domain of the given function is $(- \infty, \infty)$ and its range is $[1, \infty)$ and intercept is $(0, 1)$ .

Step by step solution

Step 1. The graph of given function is

Step 2. The domain and range of the function.

The graph of $e^{- x}$ for $x < 0$ consists of only those values of x that are negative and the graph of $e^{x}$ for $x \geq 0$ consists of only those values of x that are positive.

From the graph, it can be concluded that the domain of the function is $(- \infty, \infty)$ and the range of the function is ${x; x \geq 1}$ or $[1, \infty)$ . The intercept for the given function is $(0, 1)$ .

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In Problems $97 - 100$ , graph each function. Based on the graph, state the domain and the range and find any intercepts.
$f (x) = \{\begin{cases} e^{- x} i f x < 0 \\ e^{x} i f x \geq 0 \end{cases}$

Short Answer

Step by step solution

Step 1. The graph of given function is

Step 2. The domain and range of the function.

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In Problems 97-100, graph each function. Based on the graph, state the domain and the range and find any intercepts.f(x)=e-xifx<0exifx≥0

Short Answer

Step by step solution

Step 1. The graph of given function is

Step 2. The domain and range of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems $97 - 100$ , graph each function. Based on the graph, state the domain and the range and find any intercepts.
$f (x) = \{\begin{cases} e^{- x} i f x < 0 \\ e^{x} i f x \geq 0 \end{cases}$