Question

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

Answer 1

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,

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

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

                                             $m_{g(x)} \ = \ \displaystyle\frac{7 \ - \ (-9)}{0 \ - \ 4} \\ \\ m_{g(x)} \ = \ -4$.

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

                                          $c_{f(x)} \ = \ 4 \ < \ c_{g(x)} \ = \ 7$