Question

cubic & cube root functions unit online practice
complete this assessment to review what you’ve learned. it will not count toward your grade
given the function $g(x) = \sqrt3{x} + 8$, what happens as $x$ approaches negative infinity? (1 point)
\\(\circ\\) $y$ approaches $-8$
\\(\circ\\) $y$ approaches $8$
\\(\circ\\) $y$ approaches negative infinity
\\(\circ\\) $y$ approaches positive infinity
check answer remaining attempts : 3
graphing calculator

Explanation:

Step1: Analyze the cube root function

The function is \( g(x)=\sqrt[3]{x}+8 \). For the cube root function \( \sqrt[3]{x} \), when \( x \) approaches negative infinity, \( \sqrt[3]{x} \) also approaches negative infinity because the cube root of a very large negative number is a very large negative number (e.g., \( \sqrt[3]{-1000}=-10 \), \( \sqrt[3]{-1000000}=-100 \), and as \( x \to -\infty \), \( \sqrt[3]{x} \to -\infty \)).

Step2: Analyze the entire function

Now, the function \( g(x) \) is \( \sqrt[3]{x}+8 \). If \( \sqrt[3]{x} \to -\infty \) as \( x \to -\infty \), then adding 8 to a quantity that approaches negative infinity will still result in the quantity approaching negative infinity. So \( g(x)=\sqrt[3]{x}+8 \) will approach negative infinity as \( x \) approaches negative infinity.

Answer:

\( y \) approaches negative infinity (the option: \( y \) approaches negative infinity)