Chapter 4: Q55. (page 274)

Graph each function. State the domain and range.
$f (x) = {\begin{cases} x - 2 if x < 1 \\ 3 x if x \geq 1 \end{cases}}$

Short Answer

Expert verified

The domain is all real numbers and the range is

${y : y \geq 3 or y < - 1}$

Step by step solution

Step 1. State the concept for the given function.

This is a piece-wise defined function. Check for different values in the domain and include the values for which the function changes :

$y = f (x) = \{\begin{matrix} x - 2; x < 1 \\ 3 x; x \geq 1 \end{matrix}\}$

Step 2. Make a table for the given function.

Construct a table for $f (x)$ by taking some values of $x$ .

$x$	$x \geq 1$	$x < 1$	$y = f (x) = \{\begin{matrix} x - 2; x < 1 \\ 3 x; x \geq 1 \end{matrix}\}$
$- 1$	No	Yes	$- 3$
0	No	Yes	$- 2$
1	Yes	No	3
2	Yes	No	6
3	Yes	No	9

Step 3. Plot the graph.

Plot the values of $x$ and $f (x)$ on a graph,

The $x$ -coordinate values specify the domain of the function. Since the graph covers all possible values of $x$ , the domain is all real numbers.

The $y$ -coordiante values specify the range of the function. Since, the graph does not take any value less than $y = 3$ and more than or equal to $y = - 1$ , the range is ${y : y \geq 3 or y < - 1}$ .

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Graph each function. State the domain and range.
$f (x) = {\begin{cases} x - 2 if x < 1 \\ 3 x if x \geq 1 \end{cases}}$

Short Answer

Step by step solution

Step 1. State the concept for the given function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

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Graph each function. State the domain and range.f(x)={x−2ifx<13xifx≥1}

Short Answer

Step by step solution

Step 1. State the concept for the given function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.
$f (x) = {\begin{cases} x - 2 if x < 1 \\ 3 x if x \geq 1 \end{cases}}$