Question

question 8 of 10
the graph of g(x), shown below, resembles the graph of f(x) = x⁴ - x², but it has been changed somewhat. which of the following could be the equation of g(x)?
a. g(x) = x⁴ - x² + 0.5
b. g(x) = (x - 0.5)⁴ - (x - 0.5)²
c. g(x) = x⁴ - x² - 0.5
d. g(x) = (x + 0.5)⁴ - (x + 0.5)²

Explanation:

Step1: Analyze vertical shift

The graph of \(g(x)\) is above \(f(x)=x^4 - x^2\), so it’s shifted up. A vertical shift up by \(c\) is \(f(x)+c\).

Step2: Match with options

Option A is \(x^4 - x^2 + 0.5\), which is \(f(x)+0.5\) (shift up 0.5). Others are shifts left/right or down.

Answer:

A. \(g(x) = x^4 - x^2 + 0.5\)