Question

& cube root functions graphing the cube root function back to intro page f(x) = \sqrt3{x} -10 -5 0 5 -5 click for long desc using the graph of the function f(x) = \sqrt3{x}, what happens as x approaches negative infinity? (1 point) \bigcirc y approaches 0 \bigcirc y approaches negative infinity \bigcirc y approaches -3 \bigcirc y approaches infinity

Explanation:

Step1: Analyze the cube root function graph

The function is \( f(x)=\sqrt[3]{x} \). Looking at the graph, as \( x \) moves towards negative infinity (left on the x - axis), observe the y - values of the graph.

Step2: Determine the trend of y

For the cube root function \( y = \sqrt[3]{x}\), when \( x\to-\infty\), we know from the properties of the cube root function (and also from the graph) that as \( x\) becomes more and more negative, \( y=\sqrt[3]{x}\) also becomes more and more negative. So \( y\) approaches negative infinity. Also, by looking at the left - most part of the graph (where \( x\) is very negative), the \( y\) - values of the graph are decreasing towards negative infinity.

Answer:

B. \( y \) approaches negative infinity (assuming the option "y approaches negative infinity" is option B, if the original options had labels like A, B, C, D, we would use the correct label with the text. Since in the given options, the second option is "y approaches negative infinity", we select that. If we consider the options as:

1. \( y \) approaches 0
2. \( y \) approaches negative infinity
3. \( y \) approaches - 3
4. \( y \) approaches infinity

Then the correct answer is the second option: \( y \) approaches negative infinity)