Step-by-step explanation:
The function f(x) is defined as a line with a slope of -3 and a y-intercept of 4, hence following the definition of the slope-intercept form of a line,
.
Similarly, for g(x) as shown in the graph. First, to find the slope of the line defined by g(x),
.
Moreover, it is given that the line passes through the point (0, 7) which is the y-intercept of g(x). Thus,
It is known that all polynomial functions are defined everywhere along the real number line and since both functions, <em>f</em> and <em>g</em>, are polynomial functions of the 1st degree, represented by the general form of the function
where is the slope of the line and
is the y-intercept (the y-coordinate of the point in which the line intersects the y-axis) of the linear function with their domains following the set
.
Furthermore, both functions <em>f</em> and <em>g</em> have no points of discontinuity (no points where the function is not defined). Hence, the range of functions <em>f</em> and <em>g</em> is
.
It is shown above that when the slope of and
are compared, the following inequality describes the relationship.
whereas the comparison of the y-intercept, , of both functions is explained by the inequality