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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.

Respuesta :

MissPhiladelphia
"The graph would shift 5 units to the left" is the one among the following choices given in the question that describes what would happen to the graph if (x + 5) was substituted in place of the x. The correct option among all the options that are given in the question is the last option or the fourth option or option "D".

Answer:

Option: D is the correct answer.

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

Step-by-step explanation:

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:

          [tex]y=x^2+5x-2[/tex] is converted to:

[tex]y=(x+5)^2+5(x+5)-2[/tex]

Here we have a=5>0

            Hence, the shift is 5 units to the left.

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