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defon
3 years ago
14

PLEASE HELP I AM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100 PTS!!!

Mathematics
1 answer:
laiz [17]3 years ago
6 0

Answer:

  • A and D

Step-by-step explanation:

<u>Let the functions be</u>

  • f(x)= ax + b
  • g(x) = cx + d

<u>Their sum</u>

  • j(x) = (a+c)x + b+d

<u>Their product</u>

  • k(x)= (ax + b)(cx + d)
<h3>The answer options</h3>

<u>A. When added, the sum of the y-intercepts must be 1. </u>

  • Correct. We see point (0,1) of j(x) on the graph. b+d = 1

<u>B. When multiplied, the product of the y-intercepts must be –15. </u>

  • 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)

<u>C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change. </u>

  • 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.

<u>D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2. </u>

  • 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)

<u>E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.</u>

  • Incorrect. It should result in decreasing function of j(x) with slope of -4 but it is increasing as per graph.
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