Question

question 6 (1 point)
if ( f(x) ) is a non-constant linear function and ( g(x) ) is a quadratic function, then what type of function is ( y = f(x)g(x) )?

a) linear

b) cubic

c) quadratic

d) cannot be determined for sure

Explanation:

Step1: Recall function forms

A linear function \( f(x) \) has the form \( f(x)=ax + b \) (\( a
eq0 \), since non - constant). A quadratic function \( g(x) \) has the form \( g(x)=cx^{2}+dx + e \) (\( c
eq0 \)).

Step2: Multiply the two functions

Multiply \( f(x) \) and \( g(x) \):

$$
LATEXBLOCK0
$$

Since \( a
eq0 \) and \( c
eq0 \), the coefficient of \( x^{3} \) (i.e., \( ac \)) is non - zero. A function of the form \( y = Ax^{3}+Bx^{2}+Cx + D \) (\( A
eq0 \)) is a cubic function.

Answer:

b) cubic