The sum and product of two linear functions are shown Which statements can be used to describe the original functions f(x) and g(x)? Select three options.
When added, the sum of the y intercepts must be 8.
When multiplied, the product of the y-intercepts must be 8.
Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3.
f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1.

The statements that can be used to describe the original functions f(x) and g(x) are when added, the sum of the y-intercepts must be 8. The correct option is B.

What is a function?

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

It is given that sum and product of two linear functions are shown in the image which is attached with the answer below;-

The statements that can be used to describe the original functions f(x) and g(x) will be calculated as below:-

Let the functions be:-

f(x) = ax + b

g(x) = cx + d

Their sum is;

j(x) = (a + c)x + b + d

Their product is;

k(x) = (ax + b)(cx + d)

From the graph, we see that;

f(x) = x + 6

g(x) = -2x² + 8

f'(x) = 1

g'(x) = -4x

Therefore, the statements that can be used to describe the original functions f(x) and g(x) are when added, the sum of the y-intercepts must be 8. The correct option is B.