Truthful lips endure forever, but a lying tongue lasts only a moment. Proverbs 12:19 NIV
2-Review
Take this test as you would take a test in class. When you are finished, check your work against the answers.
Simplify
- (2 − i) + (−4 + 3i)
- (2 − i)(−4 + 3i)
- \(\frac{2-i}{-4+3i}\)
- 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) = x2.
- Describe the left and right-hand end behavior of f(x) = x9 − 16x.
- Divide with long division (3x3 + 2x − 4) ÷ (3x + 1).
- Divide with synthetic division (2x3 + x2 − 3x + 10) ÷ (x − 1).
- Use the Factor Theorem to find all the real zeros for the given polynomial function and one factor: x3 + x2 − 14x − 24; x + 2
For the following questions use f(x) = x4 + x3 − 3x2 + 9x − 108.
- 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).
Find the intercepts and asymptotes of the following functions.
- \(f(x) = \frac{x+3}{x^2-4x+3}\)
- \(f(x) = \frac{x^2-64}{x^2-4}\)
- \(f(x) = \frac{x^2 + 7x + 12}{x-2}\)
Graph the following functions.
- \(f(x) = \frac{x+3}{x^2-4x+3}\)
- \(f(x) = \frac{x^2-64}{x^2-4}\)
- \(f(x) = \frac{x^2+7x+12}{x-2}\)
Solve the nonlinear inequalities.
- x2 + 5x + 9 > 5
- \(\frac{x+10}{x-7}+1 ≤ 0\)
Answers
- −2 + 2i
- −5 + 10i
- \(\frac{-11-2i}{25}\)
- 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
- ±3i
- f(x) = 2x3 − 6x + 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)