Question

unit: functions progress: the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. given ( f(x) = 3x - 5 ), find ( f(x + 2) ). ( circ f(x + 2) = 3x^2 + x - 10 ) ( circ f(x + 2) = 3x + 1 ) ( circ f(x + 2) = x - 3 ) ( circ f(x + 2) = 3x - 3 )

Explanation:

Step1: Substitute \( x + 2 \) into \( f(x) \)

Given \( f(x) = 3x - 5 \), to find \( f(x + 2) \), we replace every \( x \) in \( f(x) \) with \( x + 2 \). So we get \( f(x + 2)=3(x + 2)-5 \).

Step2: Simplify the expression

First, expand \( 3(x + 2) \) using the distributive property: \( 3(x + 2)=3x+6 \). Then subtract 5: \( 3x + 6 - 5 = 3x + 1 \)? Wait, no, wait, let's recalculate. Wait, \( 3(x + 2)-5 = 3x+6 - 5=3x + 1 \)? Wait, no, the options have \( 3x - 3 \). Wait, maybe I made a mistake. Wait, no, let's check again. Wait, \( f(x)=3x - 5 \), so \( f(x + 2)=3(x + 2)-5=3x+6 - 5=3x + 1 \)? But the options have \( f(x + 2)=3x - 3 \)? Wait, no, maybe the original function is \( f(x)=3x - 5 \), so when we substitute \( x+2 \), it's \( 3(x + 2)-5 = 3x + 6 - 5 = 3x + 1 \)? But the options: let's check the options again. The options are:

1. \( f(x + 2)=3x^2 + x - 10 \)

1. \( f(x + 2)=3x + 1 \)

1. \( f(x + 2)=x - 3 \)

1. \( f(x + 2)=3x - 3 \)

Wait, maybe I miscalculated. Wait, \( 3(x + 2)-5 = 3x + 6 - 5 = 3x + 1 \), which is the second option. Wait, but let's check again. If \( f(x)=3x - 5 \), then \( f(x + 2)=3(x + 2)-5 = 3x + 6 - 5 = 3x + 1 \). So the correct option is the one with \( 3x + 1 \).

Answer:

The correct option is the one with \( f(x + 2) = 3x + 1 \) (the second option among the given choices).