Question

Graph the recursive function below, complete the table of values, and rewrite it as an explicit function (slope-intercept or point slope) 푎 0 = − 6; 푎 푛 = 푎 푛−1 + 2.5

Answer 1

To graph the recursive function and complete the table of values, we can start with the given initial value of a_0 = -6 and use the recursive formula a_n = a_(n-1) + 2.5 to generate the subsequent terms.

Table of values:
n | a_n
------------
0 | -6
1 | -6 + 2.5 = -3.5
2 | -3.5 + 2.5 = -1
3 | -1 + 2.5 = 1.5
4 | 1.5 + 2.5 = 4
5 | 4 + 2.5 = 6.5
...

To graph the function, we plot the values from the table of values on a coordinate plane.

The explicit function can be found by noticing the pattern in the recursive formula. Each term is obtained by adding 2.5 to the previous term. This suggests a linear relationship.

Let's assume the explicit function is of the form:
a_n = m*n + b

To find the values of m and b, we can substitute a_0 = -6 into the explicit function equation:
-6 = m*0 + b
b = -6

Therefore, the explicit function for the recursive formula a_n = a_(n-1) + 2.5 is:
a_n = 2.5n - 6