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# College algebra: final exam

6. Find the equation of the circle centered at $(-1,-1)$ and passing through the point $(-1,1).$

7. Find the composition \ $h(x)=(g\circ f)(x)$ of the functions $y=f(x)=x^{2}-1$ and $g(y)=3y-1.$ Evaluate $h(1).$

8. The perimeter of a rectangle is 10 sq. feet. (a) Express the area of the rectangle in terms of its width. (b) Find the maximal possible area.

9. Given $f(x)=-(x-3)^{4}(x+1)^{3}$. Find the leading term and use it to describe the long term behavior of the function.

10. The graph of the function $y=f(x)$ is given below. (1) Find its domain. (2) Determine intervals on which the function is decreasing or increasing. (3) Provide $x$-coordinates of its relative maxima and minima. $(4)$ Find its asymptotes.