Question

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study paths tx math bridge - stage 2 unit test: functi
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unit: functions
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given f(x) = 6x + 2, find f(x - 3).
f(x - 3) = 6x - 1
f(x - 3) = x - 1
f(x - 3) = 6x - 16
f(x - 3) = 6x² - 16x - 6
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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 " \( f(x - 3)=6x - 16 \)")