amarieon999
Answered

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The function [tex]\( f(x) = x^2 + 5x - 6 \)[/tex] is shifted 4 units to the left to create [tex]\( g(x) \)[/tex]. What is [tex]\( g(x) \)[/tex]?

A. [tex]\( g(x) = (x-4)^2 + 5(x-4) - 6 \)[/tex]

B. [tex]\( g(x) = (x+4)^2 + 5(x+4) - 6 \)[/tex]

C. [tex]\( g(x) = \left(x^2 + 5x - 6\right) - 4 \)[/tex]

D. [tex]\( g(x) = \left(x^2 + 5x - 6\right) + 4 \)[/tex]

Sagot :

GinnyAnswer
To shift the function [tex]\(f(x) = x^2 + 5x - 6\)[/tex] 4 units to the left, we replace [tex]\(x\)[/tex] with [tex]\(x + 4\)[/tex] in the function.

The new function [tex]\(g(x)\)[/tex] is obtained by substituting [tex]\(x + 4\)[/tex] into [tex]\(f(x)\)[/tex]:
[tex]\[ g(x) = f(x + 4) \][/tex]

Let's perform this substitution step-by-step:

1. Replace every [tex]\(x\)[/tex] in [tex]\(f(x)\)[/tex] with [tex]\(x + 4\)[/tex]:
[tex]\[ f(x + 4) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]

Thus, the function [tex]\(g(x)\)[/tex] is:
[tex]\[ g(x) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]

This matches option B:
[tex]\[ g(x) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
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