Use a graphing calculator to find, approximately the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + 2 x - 10$
A) $[ 0 , \infty )$
B) $( - \infty , \infty )$
C) $[ - 10,10 )$
D) $[ - \infty , 5 )$
E) $[ - 10 , \infty )$

Question

Quizplus · Accepted Answer

By graphing the function on a graphing calculator, we can see that the range of the function is approximately from $-10$ to $\infty$. To be more precise, the function approaches $-\infty$ as $x$ approaches $-\infty$, and as $x$ approaches approximately $1.5$ from the left, the function approaches $-\infty$ again. After this point, the function increases without bound, so the range is approximately $[-10,\infty)$. Therefore, the answer is choice E.

Use a Graphing Calculator to Find, Approximately the Range of the Function