texascollegebridge\nstudy paths tx math bridge - stage 2 unit test: functi\nf\nunit: functions\nprogress:\nth…

texascollegebridge\nstudy paths tx math bridge - stage 2 unit test: functi\nf\nunit: functions\nprogress:\nthe movement of the progress bar may be uneven because questions can be worth more c\ngiven f(x) = 6x + 2, find f(x - 3).\n f(x - 3) = 6x - 1\n f(x - 3) = x - 1\n f(x - 3) = 6x - 16\n f(x - 3) = 6x² - 16x - 6\n64°f\nclear\nsearch

texascollegebridge\nstudy paths tx math bridge - stage 2 unit test: functi\nf\nunit: functions\nprogress:\nthe movement of the progress bar may be uneven because questions can be worth more c\ngiven f(x) = 6x + 2, find f(x - 3).\n f(x - 3) = 6x - 1\n f(x - 3) = x - 1\n f(x - 3) = 6x - 16\n f(x - 3) = 6x² - 16x - 6\n64°f\nclear\nsearch

Answer

Explanation:

Step1: Substitute ( x - 3 ) into ( f(x) )

To find ( f(x - 3) ), we substitute ( x ) with ( x - 3 ) in the function ( f(x) = 6x + 2 ). So we get ( f(x - 3)=6(x - 3)+2 ).

Step2: Distribute and simplify

First, distribute the 6 in ( 6(x - 3) ): ( 6(x - 3)=6x-18 ). Then add 2: ( 6x - 18+2 = 6x-16 )? Wait, no, wait, let's recalculate. Wait, ( 6(x - 3)+2=6x-18 + 2=6x-16 )? Wait, no, that's not right. Wait, no, wait, ( 6(x - 3)=6x - 18 ), then ( 6x-18 + 2=6x-16 )? Wait, but let's check again. Wait, the original function is ( f(x)=6x + 2 ). So substituting ( x-3 ) for ( x ), we have ( f(x - 3)=6(x - 3)+2 ). Let's compute that: ( 6x-18 + 2=6x-16 )? Wait, no, wait, -18 + 2 is -16? Wait, no, -18 + 2 is -16? Wait, 18 - 2 is 16, so -18 + 2 is -16. So ( f(x - 3)=6x-16 )? Wait, but let's check the options. Wait, no, wait, maybe I made a mistake. Wait, no, let's do it again. ( f(x)=6x + 2 ). So ( f(x - 3)=6(x - 3)+2=6x-18 + 2=6x-16 ). Wait, but the first option is ( 6x - 1 ), that's wrong. Wait, no, wait, maybe I misread the function. Wait, the function is ( f(x)=6x + 2 )? Or is it ( f(x)=6x + 2 )? Wait, let's check the substitution again. ( f(x - 3)=6(x - 3)+2=6x-18 + 2=6x-16 ). So the third option is ( f(x - 3)=6x - 16 ), which matches. Wait, but let's check the calculation again. Wait, 6 times (x - 3) is 6x - 18, plus 2 is 6x - 16. So the correct answer is ( f(x - 3)=6x - 16 ), which is the third option. Wait, but wait, maybe the function was ( f(x)=6x + 2 ), so substitution gives ( 6(x - 3)+2=6x-18 + 2=6x-16 ). So the third option is correct.

Wait, no, wait, I think I made a mistake earlier. Wait, let's recalculate: ( 6(x - 3)=6x - 18 ), then ( 6x - 18 + 2 = 6x - 16 ). Yes, that's correct. So the correct answer is ( f(x - 3)=6x - 16 ), which is the third option.

Answer:

( f(x - 3)=6x - 16 ) (corresponding to the option " ( f(x - 3)=6x - 16 )")