What is the Range of the following cube root function \( f(x)=2 \sqrt[3]{x+1}-4 \)
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The cube root function has a unique property: its range is all real numbers! So, for the function \( f(x)=2 \sqrt[3]{x+1}-4 \), as \( x \) takes on any value from negative to positive infinity, the cube root will also span all values. After scaling by 2 and shifting down by 4, you'll still cover all real numbers. In simpler terms, no matter what, \( f(x) \) can output every possible value. If you were to visualize this function, you'd notice that it approaches negative infinity as \( x \) tends to negative infinity, and it moves towards positive infinity as \( x \) goes to positive infinity. That’s how the magic of cube roots works alongside linear transformations!