Question

Please I need this ASAP I will give a lot of points if I get the right answer thank you

Answer 1

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,

`f(x) \ = \ -3x \ + \ 4`.

Similarly, for g(x) as shown in the graph. First, to find the slope of the line defined by g(x),

`m_(g(x)) \ = \ \displaystyle(7 \ - \ (-9))/(0 \ - \ 4) \\ \\ m_(g(x)) \ = \ -4`.

Moreover, it is given that the line passes through the point (0, 7) which is the y-intercept of g(x). Thus,

`g(x) \ = \ -4x \ + \ 7`

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

`f(x) \ = \ mx \ + \ c,`

where
`m` is the slope of the line and
`c` 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
`\{x \ | \ x \in \mathbb{R} \}`.

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

`\{ x \ | \ x \ \in \ \mathbb{R} \}`.

It is shown above that when the slope of
`f(x)` and
`g(x)` are compared, the following inequality describes the relationship.

`m_(f(x)) \ = \ -3 \ > \ m_(g(x)) \ = \ -4`

whereas the comparison of the y-intercept,
`c`, of both functions is explained by the inequality

`c_(f(x)) \ = \ 4 \ < \ c_(g(x)) \ = \ 7`