Answer:
Step-by-step explanation:
Let the functions be
- f(x)= ax + b
- g(x) = cx + d
Their sum
Their product
The answer options
A. When added, the sum of the y-intercepts must be 1.
- Correct. We see point (0,1) of j(x) on the graph. b+d = 1
B. When multiplied, the product of the y-intercepts must be –15.
- Incorrect. -15 is the vertex of k(x). The vertex of ax^2 + bx + c is -b/2a. So it has no relation to constants of the functions f(x) and g(x)
C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
- Incorrect. It refers to the value of ac. If one of a or c has opposite sign it makes k(x) to open down but it is not as per graph.
D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
- Correct. As per above statement, both linear equations could be positive as their sum and product is positive from the graphs of j(x) and k(x)
E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.
- Incorrect. It should result in decreasing function of j(x) with slope of -4 but it is increasing as per graph.
