Question

Which of the following is a true statement

Answer 1

Function f(x) is a quadratic equation and function g(x) is a linear equation. (Correct choice: D)

How to determine the nature of two functions

In this problem we find two functions, one in the form of a equation and other in the form of a table. The first equation is clearly a quadratic equation, that is, an equation of the form:

f(x) = a · x² + b · x + c

Where a, b, c are real coefficients.

And the second function is a linear equation if and only if slope is the same for every pair of points. This can be checked by means of secant line formula:

`m = (\Delta y)/(\Delta x)`

Now we proceed to check the condition:

`m_1 = (- 1 - (- 17))/(2 - (- 2))`

m₁ = 4

`m_2 = (- 5 - (- 9))/(1 - 0)`

m₂ = 4

m₁ = m₂ = 4

Thus, g(x) is a linear equation.