Let f( x)=2x^2+7x and g(x)=-8x^2-3x+5. What is g(x)+f(x)?
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Answer:
1. In order for Pattern B to be linear, the common difference of the number of dots between each step should be constant. As it is not constant, the pattern is not linear.
2. In order for Pattern B to be exponential, the common ratio of the number of dots between each step should be constant. As it is not constant, the pattern is not exponential.
3. In order for Pattern B to be quadratic, its sequence of second differences must be constant.
First differences:
Second differences:
Therefore, as the sequence of second difference is constant, the patten is quadratic.
The function for pattern B is:
(where x is the step number)