Consider the function y=x^2+5x-2 . what would happen to the graph if (x + 5) was substituted in place of the x?

a. the graph would shift 5 units to the right.
b. the graph would shift down 5 units.
c. the graph would shift up 5 units.
d. the graph would shift 5 units to the left.
consider the function y=x^2+5x-2 . what would happen to the graph if (x + 5) was substituted in place of the x?

a. the graph would shift 5 units to the right.
b. the graph would shift down 5 units.
c. the graph would shift up 5 units.
d. the graph would shift 5 units to the left.

Option: D is the correct answer.

          D. The graph would shift 5 units to the left.

We know that the transformation of a function f(x) to f(x+a) is a shift of the function either to the left or to the right by a units depending on the sign of a i.e.  if a>0 then the shift is a units to the left

and if a<0 then the shift is a units to the right.

Here we have:

          is converted to:

Here we have a=5>0

            Hence, the shift is 5 units to the left.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).