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,
[tex]f(x) \ = \ -3x \ + \ 4[/tex].
Similarly, for g(x) as shown in the graph. First, to find the slope of the line defined by g(x),
[tex]m_{g(x)} \ = \ \displaystyle\frac{7 \ - \ (-9)}{0 \ - \ 4} \\ \\ m_{g(x)} \ = \ -4[/tex].
Moreover, it is given that the line passes through the point (0, 7) which is the y-intercept of g(x). Thus,
[tex]g(x) \ = \ -4x \ + \ 7[/tex]
It is known that all polynomial functions are defined everywhere along the real number line and since both functions, f and g, are polynomial functions of the 1st degree, represented by the general form of the function
[tex]f(x) \ = \ mx \ + \ c,[/tex]
where [tex]m[/tex] is the slope of the line and [tex]c[/tex] 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 [tex]\{x \ | \ x \in \mathbb{R} \}[/tex].
Furthermore, both functions f and g have no points of discontinuity (no points where the function is not defined). Hence, the range of functions f and g is
[tex]\{ x \ | \ x \ \in \ \mathbb{R} \}[/tex].
It is shown above that when the slope of [tex]f(x)[/tex] and [tex]g(x)[/tex] are compared, the following inequality describes the relationship.
[tex]m_{f(x)} \ = \ -3 \ > \ m_{g(x)} \ = \ -4[/tex]
whereas the comparison of the y-intercept, [tex]c[/tex], of both functions is explained by the inequality
[tex]c_{f(x)} \ = \ 4 \ < \ c_{g(x)} \ = \ 7[/tex]
