91Ó°ÊÓ

We have a degree of five from$f\left(x\right)=20x^4+73x^3+46x^2−52x−24â€\dots$

Thus, the graph of function has an end behavior similar to$y=20x^4$

Determine the intercept of function to get the x- intercept.

$\begin{array}{r}20x^4+73x^3+46x^2−52x−24â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =0â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots \\ (x+2{)}^2(4x−3\left)\right(5x+2)â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =0â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots \\ x+2=0;4x−3â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =0â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots 5x+2â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =0\\ x=−2;4xâ€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =3;â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots 5xâ€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =−2\\ xâ€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =\frac{3}{4};â€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots xâ€\dots â\P Ä\dots â\P Ä\dots â\P Ä\dots =−\frac{2}{5}\end{array}$

Considering$f\left(0\right)=-24$, thus y-intercept is$(0,-24)$

From the graph above, we can see that the maximum and minimum turning point of the function is:

Maximum: $(-1.048,21.119)$

Minimum:$(-2,0),(0.31,-33.34)$

Therefore, the domain of the function is the set of all real numbers and range is$(-33.34,∞)$

By observing the graph above, we say that the function at the intervals of

$(-2,-1.408),(0.31,∞)$is increasing.

At intervals of$(-∞,-2),(-1.048,0.31)$