Question

match the description with the correct response.
a function that is not linear

choose the correct answer below.
a. $f(x)=3$
b. $f(x)=3x - 2$
c. $f(x)=3x + 2$
d. $f(x)=x^3 + 2$

Explanation:

Step1: Recall linear function form

A linear function has the form \( f(x) = mx + b \), where \( m \) and \( b \) are constants, and the highest power of \( x \) is 1. A constant function (like \( f(x)=3 \)) can be written as \( f(x)=0x + 3 \), so it's also linear.

Step2: Analyze each option

• Option A: \( f(x)=3 = 0x + 3 \), linear (degree 1).
• Option B: \( f(x)=3x - 2 \), linear (degree 1).
• Option C: \( f(x)=3x + 2 \), linear (degree 1).
• Option D: \( f(x)=x^3 + 2 \), the highest power of \( x \) is 3, so it's a cubic (non - linear) function.

Answer:

D. \( f(x)=x^{3}+2 \)