Question

question 6 of 25
in which direction does the left side of the graph of this function point?
$f(x) = 3x^4 - x^2 + 4x - 2$

Explanation:

Step1: Analyze the leading term

The function is \( f(x) = 3x^4 - x^2 + 4x - 2 \). The leading term is \( 3x^4 \), where the coefficient \( a = 3 \) (positive) and the degree \( n = 4 \) (even).

Step2: Determine end - behavior for even degree

For a polynomial function \( f(x)=a_nx^n + a_{n - 1}x^{n - 1}+\cdots+a_1x + a_0 \), when \( n \) is even:

• If \( a_n>0 \), as \( x

ightarrow-\infty \) (left - hand side) and \( x
ightarrow+\infty \) (right - hand side), \( f(x)
ightarrow+\infty \).
Since \( n = 4 \) (even) and \( a = 3>0 \), as \( x
ightarrow-\infty \) (moving to the left on the x - axis), \( f(x)
ightarrow+\infty \). This means the left - hand side of the graph points upwards.

Answer:

The left side of the graph points upwards (or in the positive \( y \) - direction).