Final answer:
The graph of a function that is defined for a specific range such as 0 ≤ x ≤ 20, and has a horizontal line, showcases a constant value of f(x) within that range. The slope of the line determines its direction: a slope of 0 results in a horizontal line, while a positive or negative slope results in an upward or downward sloping line, respectively. Understanding the y-intercept and slope is fundamental in graphing linear functions.
Step-by-step explanation:
Understanding Graphs of Functions
To find the graph of a function that is defined for a certain range, has a relative point, and has an absolute value, we need to consider several aspects of function graphing. Horizontal lines in a function graph indicate that there is no change in the value of y as x changes. When a function represents a horizontal line and is defined, for instance, for 0 ≤ x ≤ 20, the value of the function (f(x)) is constant between these x-values.
Understanding the slope of a line is also crucial. If b = 0, the line is horizontal. However, if b > 0, the line will slope upward, and if b < 0, it will slope downward. Sketching a graph involves plotting specific (x,y) data pairs to represent the relation between variables.
The y-intercept is the point where the line crosses the y-axis, and the slope determines how steep the line is. For a line with a slope of 3, for every one unit increase in x there is a rise of 3 units in y. This slope is consistent along the entire line.