Final answer:
To construct a histogram, collect data and divide its range into intervals. Plot frequency bars for each interval on graph paper and scale the axes. The constant function f(x) = 10 for 0≤x≤20 will be a horizontal line from x=0 to x=20 with a domain of [0, 20] and a range of [10, 10].
Step-by-step explanation:
To construct a histogram, you will first need to collect or be provided with a set of data. Histograms represent the distribution of numerical data, where the data is grouped into ranges, called bins or intervals. Here are the step-by-step instructions on how to create a histogram:
- Determine the range of the data set (the minimum and maximum values).
- Divide the range into five to six equal intervals. Choosing the number of intervals can affect how your histogram looks, but starting with five to six is a good rule of thumb.
- Count how many data points fall into each interval.
- On graph paper, draw two axes using a ruler and pencil. The horizontal axis (x-axis) will represent the intervals, and the vertical axis (y-axis) will represent the frequency of the data within each interval.
- Label the x-axis with the intervals and the y-axis with the frequencies.
- Draw a bar for each interval that reaches up to the corresponding frequency on the y-axis.
- Make sure to appropriately scale the axes for clear representation of the data.
If you want to represent the function f(x) = 10 where 0≤x≤20, you would simply draw a horizontal line at the point where y=10 and make sure it stretches from x=0 to x=20. This line represents a constant function where the value of f(x) does not change regardless of the value of x within the given domain.
The domain and range for this function in interval notation would be:
Domain: [0, 20]
Range: [10, 10]