question 1 of 26\nthe function $f(x) = x^2 + 5x - 6$ is shifted 4 units to the left to create $g(x)$. what…

question 1 of 26\nthe function $f(x) = x^2 + 5x - 6$ is shifted 4 units to the left to create $g(x)$. what is $g(x)$?\n\na. $g(x) = (x^2 + 5x - 6) + 4$\n\nb. $g(x) = (x^2 + 5x - 6) - 4$\n\nc. $g(x) = (x + 4)^2 + 5(x + 4) - 6$\n\nd. $g(x) = (x - 4)^2 + 5(x - 4) - 6$

question 1 of 26\nthe function $f(x) = x^2 + 5x - 6$ is shifted 4 units to the left to create $g(x)$. what is $g(x)$?\n\na. $g(x) = (x^2 + 5x - 6) + 4$\n\nb. $g(x) = (x^2 + 5x - 6) - 4$\n\nc. $g(x) = (x + 4)^2 + 5(x + 4) - 6$\n\nd. $g(x) = (x - 4)^2 + 5(x - 4) - 6$

Answer

Explanation:

Step1: Recall horizontal shift rule

For a function ( y = f(x) ), shifting it ( h ) units to the left replaces ( x ) with ( x + h ) in the function. Here, ( h = 4 ), so we replace ( x ) with ( x + 4 ) in ( f(x) ).

Step2: Apply the rule to ( f(x) )

Given ( f(x)=x^{2}+5x - 6 ), substituting ( x ) with ( x + 4 ) gives ( g(x)=f(x + 4)=(x + 4)^{2}+5(x + 4)-6 ).

Answer:

C. ( g(x) = (x + 4)^{2} + 5(x + 4) - 6 )