Chapter 2: Q11. (page 93)

Graph each function. Identify the domain and range.
$h (x) = {\begin{cases} x + 3 i f x \leq - 1 \\ 2 x i f x > - 1 \end{cases}$

Short Answer

Expert verified

The domain is all real numbers.

The range is all real numbers.

Step by step solution

Step-1 – Range and Domain

The domain of the function is the set of all input values and range of the function is the set of all output values.

Step-2 – Draw the graph.

The given function is $h (x) = {\begin{cases} x + 3 i f x \leq - 1 \\ 2 x i f x > - 1 \end{cases}$

The graph of the equation $h (x) = x + 3$ is linear equation for $x \leq - 1$ .

Here, $- 1$ satisfies the inequality $x \leq - 1$ . Therefore, end with a closed circle at $x = - 1$ .

The graph of the equation $h (x) = 2 x$ is linear function for $x > - 1$ .

Here, $- 1$ not satisfies the inequality $x > - 1$ . Therefore, start with an open circle at $x = - 1$ .

Step-3 – Determine the domain and range.

The domain is all real numbers.

The range is all real numbers.

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Graph each function. Identify the domain and range.
$h (x) = {\begin{cases} x + 3 i f x \leq - 1 \\ 2 x i f x > - 1 \end{cases}$

Short Answer

Step by step solution

Step-1 – Range and Domain

Step-2 – Draw the graph.

Step-3 – Determine the domain and range.

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Column A	Column B
The slope of linem	1

Graph each function. Identify the domain and range.h(x)={x+3 if x≤−12x if x>−1

Short Answer

Step by step solution

Step-1 – Range and Domain

Step-2 – Draw the graph.

Step-3 – Determine the domain and range.

One App. One Place for Learning.

Most popular questions from this chapter

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Graph each function. Identify the domain and range.
$h (x) = {\begin{cases} x + 3 i f x \leq - 1 \\ 2 x i f x > - 1 \end{cases}$