Precalculus Exam

Simplify the rational expression.  $\frac{8x-5}{2x+3}-\frac{4x+7}{x-4}$  

•  $\frac{16x^2-11x+41}{8x^2-5x-12}$  

•  $\frac{16x^2-63x-1}{8x^2-5x-12}$  

•  $\frac{-11x+41}{8x^2-5x-12}$  

•  $\frac{-63x-1}{8x^2-5x-12}$  

Simplify the complex fraction.  $\frac{\frac{2}{x}-5}{3+\frac{7}{x-4}}$  

•  $\frac{-5x^2-18x+8}{3x^2+19x}$  

•  $\frac{x^2-3x+5}{2x^2+7x}$  

•  $\frac{2-5x}{3x+7}$  

Factor the expression completely.  $7x^3-63x+3x^2-27$  

•  $\left(7x+3\right)\left(x^2-9\right)$  

•  $\left(7x+3\right)\left(x+3\right)\left(x-3\right)$  

•  $\left(3x+7\right)\left(x^2+9\right)$  

•  $\left(x+2\right)\left(x-4\right)\left(7x-5\right)$  

Divide the polynomial.  $\frac{6x^4+7x^3+x^2-16}{2x+3}$  

•  $5x^3-4x^2+7x+3+\frac{6}{2x+3}$  

•  $3x^3-2x^2+4x+8+\frac{7}{2x+3}$  

•  $2x^3-3x^2+2x-3+\frac{8}{2x+3}$  

•  $3x^3-x^2+2x-3+\frac{-7}{2x+3}$  

Express the given series using sigma notation. 5 + 11 + 17 + ... + 95

• $\sum_{n=0}^{15}\left(6n+5\right)$

• $\sum_{n=0}^{16}\left(6n+5\right)$

• $\sum_{n=0}^{15}\left(5n+6\right)$

• $\sum_{n=0}^{16}\left(5n+6\right)$

Write an equation in standard form for the function with roots at x = 8 and x = 7i.

• $y=x^2-8x-7ix+56i$

• $y=x^3+3x^2-5x+56$

• $y=x^3-8x^2+49x-392$

Describe the end behavior of the function.  $f\left(x\right)=\left(\frac{1}{2}\right)^x$  

•  $as\ x\rightarrow-\infty,\ y\rightarrow\infty\ and\ as\ x\rightarrow\infty,\ y\rightarrow0$  

•  $as\ x\rightarrow-\infty,\ y\rightarrow0\ and\ as\ x\rightarrow\infty,\ y\rightarrow\infty$  

•  $as\ x\rightarrow-\infty,\ y\rightarrow-\infty\ and\ as\ x\rightarrow\infty,\ y\rightarrow0$  

Write the equation in factored form for the function that meets the following criteria. The graph passes through the x-axis at x=5 and x=-4. It also "bounces off" the x-axis at x=2. The graph also passes through (6, 280).

• $y=\left(x-5\right)\left(x+4\right)\left(x-2\right)^2$

• $y=2\left(x-5\right)\left(x+4\right)\left(x-2\right)^2$

• $y=1.5\left(x-5\right)\left(x+4\right)\left(x-2\right)^2$

• $y=1.75\left(x-5\right)\left(x+4\right)\left(x-2\right)^2$

Find all of the roots of the function.  $g\left(x\right)=x^4-x^3+19x^2-25x-150$  

• 3

• -2

•  $\pm i$  

•  $\pm5i$  

• -3

Write an equation with a parent function of  $f\left(x\right)=x^3$  , a horizontal shift of 7 left, a vertical shift of 2 down and a vertical stretch of magnitude 9.

•  $f\left(x\right)=\left(9x+7\right)^3-2$  

•  $f\left(x\right)=9\left(x+7\right)^3-2$  

•  $f\left(x\right)=9\left(x-7\right)^3+2$