Chapter 4.7, Problem 31PPS

To determine

To Find :

The domain and range.

Answer to Problem 31PPS

Domain is all real numbers.

Range = $\{y:y\ge 4\}$

Explanation of Solution

Given Information:

The graph is given below:

  

Concept Used:

Let the function be:

  $f(x)=y$

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out.

DOMAIN:

The domain is the set of all possible  x -values which will make the function "work", and will output real  y -values.

HOW TO FIND DOMAIN:

In general, we determine the DOMAIN of each function by looking for those values of the independent variable (usually  x ) which we are allowed to use. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign).

RANGE:

The range is the resulting  y- values we get after substituting all the possible  x -values.

HOW TO FIND RANGE:

• The RANGE of a function is the spread of possible  y -values (minimum  y -value to maximum  y -value)
• Substitute different  x -values into the expression for  y  to see what is happening.
• Make sure you look for minimum and maximum values of  y .

  

Calculation :

This is absolute value function with minimum value at y = 4.

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 = 4 , the range is = $\left\{y:y\ge 4\right\}$