Answer:
OPTION D: The rate of change of Function 2 is less than that of Function 1.
Step-by-step explanation:
From the table, we will determine the equation of function 2.
From the table, g(1) = 14 & g(-3) = - 86
Since, it is a linear function it should have been of the form, y = a + bx.
We will denote Function 2 as g(x).
So, g(1) = 14 = a + b . . . (1)
And g(-3) = -86 = -3a + b . . . (2)
From (1), a = 14 - b
Substituting this in (2), we get:
-86 = -3(14 - b) + b
⇒ - 86 = - 42 + 4b
⇒ - 44 = 4b
⇒ b = -11
So, a = 14 - (-11)
⇒ a = 25
So, equation of function 2 is: y = 25 - 11x.
Hence, Option A and B are eliminated.
In a linear equation of the form, y = ax + b, y - intercept = b.
So, in function 1, y - intercept = 19
And in function 2, y - intercept = -11
Clearly, OPTION C can be eliminated.
Now, rate of change of Function 1 = [tex]$ \frac{dy}{dx} = 30$[/tex]
and rate of change of Function 2 = [tex]$ \frac{dy}{dx} = 25 $[/tex]
Therefore, we can say that the rate of change if function 2 is less than that of function 1.
Option D is our answer.
