Precalculus by Richard Wright

Truthful lips endure forever, but a lying tongue lasts only a moment. Proverbs 12:19 NIV

Take this test as you would take a test in class. When you are finished, check your work against the answers.

- (2 −
*i*) + (−4 + 3*i*) - (2 −
*i*)(−4 + 3*i*) - \(\frac{2-i}{-4+3i}\)
- Write the equation of the parabola with a maximum at (9, 1) and goes through the point (8, −1).
- Describe how the graph of
*g*(*x*) = 2(*x*+ 3)^{2}+ 4 is transformed from*f*(*x*) =*x*^{2}. - Describe the left and right-hand end behavior of
*f*(*x*) =*x*^{9}− 16*x*. - Divide with long division (3
*x*^{3}+ 2*x*− 4) ÷ (3*x*+ 1). - Divide with synthetic division (2
*x*^{3}+*x*^{2}− 3*x*+ 10) ÷ (*x*− 1). - Use the Factor Theorem to find all the real zeros for the given polynomial function and one factor:
*x*^{3}+*x*^{2}− 14*x*− 24;*x*+ 2 - List all the
*p*'s,*q*'s, and possible rational zeros of*f*(*x*). - Find all the rational zeros of
*f*(*x*). - Find the rest of the zeros of
*f*(*x*) including any complex zeros. - Find a polynomial function with real coefficients that has the following zeros: 1 (with multiplicity 2) and −2 and (2,
*f*(2)) = (2, 8). - \(f(x) = \frac{x+3}{x^2-4x+3}\)
- \(f(x) = \frac{x^2-64}{x^2-4}\)
- \(f(x) = \frac{x^2 + 7x + 12}{x-2}\)
- \(f(x) = \frac{x+3}{x^2-4x+3}\)
- \(f(x) = \frac{x^2-64}{x^2-4}\)
- \(f(x) = \frac{x^2+7x+12}{x-2}\)
*x*^{2}+ 5*x*+ 9 > 5- \(\frac{x+10}{x-7}+1 ≤ 0\)

Simplify

For the following questions use *f*(*x*) = *x*^{4} + *x*^{3} − 3*x*^{2} + 9*x* − 108.

Find the intercepts and asymptotes of the following functions.

Graph the following functions.

Solve the nonlinear inequalities.

- −2 + 2
*i* - −5 + 10
*i* - \(\frac{-11-2i}{25}\)
*y*= −2(*x*− 9)^{2}+ 1- Vertical stretch by a factor of 2, shifted left 3 and up 4
- Falls to the left, rises to the right
- \(x^2-\frac{1}{3}x+\frac{7}{9}+\frac{-43}{9(3x+1)}\)
- \(2x^2+3x+\frac{10}{x-1}\)
- −3, −2, 4
*p*= ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±27, ±36, ±54, ±108

*q*= ±1

^{p}⁄_{q}= ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±27, ±36, ±54, ±108- −4, 3
- ±3
*i* *f*(*x*) = 2*x*^{3}− 6*x*+ 4*x*-int: −3;*y*-int: 1; VA:*x*= 1, 3; HA:*y*= 0*x*-int: −8, 8;*y*-int: 16; HA:*x*= −2, 2; HA:*y*= 1*x*-int: −4, −3;*y*-int: −6; VA:*x*= 2; SlantA:*y*=*x*+ 9- (−∞, −4) ∪ (−1, ∞)
- [−3⁄2, 7)