Given the functions f(x) = −2x − 1 and g(x) = −3x + 4, which operation results in the smallest coefficient on the x term?

There are 3 different operations we can perform. Addition, Subtractions and Multiplication.

Subtraction
(−2x − 1) - (−3x + 4)
x - 5
x coefficient = 1

Addition: 
(−2x − 1) + (−3x + 4)
3 - 5x
x coefficient = -5

Multiplication:
x(6x - 5) -4
x coefficient = 6

-5 is the least so addition is the answer

From the above observation we can conclude that as the input increases the output increases at first until it reaches a maximum after the maximum the output decreases as the input increases.

Hence, the option A is correct.

Step-by-step explanation:

Lets analyze the graph.

From the interval x = -4 to x = 2 (as the input value increases), it is clear that the output value also increases at first.

At x = 2.5, the value of y = 7 which is a maximum output value.

From the interval x = 3 to x = 10 (as the input increases) the the output value

tend to decrease from maximum y = 7 to y = -10.

So, from the above observation we can conclude that as the input increases the output increases at first until it reaches a maximum after the maximum the output decreases as the input increases.

Hence, the option A is correct.