Factor the polynomial f(x) Then solve the equation f(x)=0 f(x)=x^3-9x^2+11x+21 The factored form is f(x)=(x+1)(x-3)(x-7) The solution(s) to f(x)=0 is(are) x=-1,3,7 (Use commas to separate answers as needed. If a solution occurs more than once, type the solution only once.)

Show algebraically that f and g are inverse functions. (Example 3) 30 $f(x)=\frac {x^{2}}{4}+8,x\geqslant 0$ $g(x)=\sqrt {4x-32}$

Find the higher-order derivative. See Examples 1 and 3. $f^{(4)}(x)=(x^{2}+6)^{2}$ $f^{(6)}(x)=\square $

Determine the equation of the slant asymptote for the equation $f(x)=\frac {x^{2}+3}{x-1}$ Give your answer in the form ' $y=mx+b'$ Provide your answer below: $y=\square $

Find the inverse of $f(x)=\frac {-3x+3}{-4x+2}$ $f^{-1}(x)=\square $

16 The sum of a rational and irrational number is a(n) $\square $ number.

Is the first number is divisible by the second number? $736,652;9$ No Yes

Several equations are given illustrating a suspected number pattern. Determine what the next equation would be,and verify that it is indeed a true statement. $2^{2}-1^{2}=2+1$ $3^{2}-2^{2}=3+2$ $4^{2}-3^{2}=4+3$ Select the correct choice below and fill in the answer box to complete your choice. (Type an equation, Do not simplify.) A. The next equation would be $\square $ , but it is a false statement. B. The next equation would be $\square $ , and it is a true statement.

(1) Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. $32k^{4}+22k^{3}-9k-33$ $\square $

If $f(x,y)=sin(x)+sin(y)$ then $-\sqrt {2}\leqslant D_{u}f\leqslant \sqrt {2}$ True False

\[ \begin{array}{c} 7 / 10 \\ -14+(-3) \end{array} \] Type your answer.