Question

Two linear functions of x are shown. Which Statement about the functions is true?

Answer 1

OPTION D: The rate of change of Function 2 is less than that of Function 1.

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 =
`$ (dy)/(dx) = 30$`

and rate of change of Function 2 =
`$ (dy)/(dx) = 25 $`

Therefore, we can say that the rate of change if function 2 is less than that of function 1.

Option D is our answer.