1. Determine the equation of the line passing through the point (2, -­‐3) and parallel to the line: 4x + 3y = 5. 2. Determine: f(a+3) if 2
2x − 1
f (x) =
x + 4 3. Determine the domain and range: a.) f (x) = x − 4 2
b.) g(x) = (x − 2) + 1 4. Determine the POSSIBLE rational roots of: 5
4
3
2
f (x) = x + 2x − 3x − 4x + 5x + 6 5. Find all the zeros of: 3
2
P(x) = 2x + x + 8x + 4 6. Find all the zeros: 4
2
f
(x)
=
x
+
2x
− 15 3
2
g(x)
=
3x
+
4x
− 5x − 2
7. Factor: given that x + 2 is a factor. 8. Use the calculator to determine the relative max and min of the 3
2
f
(x)
=
x
−
5x
+ 1 function: (round to 3 decimal places). 9. Determine the equation of the parabola with vertex (-­‐2, ½ ) passing through the point (3/2 , -­‐1). Also determine if the parabola opens up or down. 10. Given: f (x) = −2 2x − 3 determine: a.) f(4) b.) f(5/2) 11. Determine the vertex and the intercepts of the parabola: f (x) = −2x 2 + 3x + 1 12. Describe the end behavior of the functions: 3
f
(x)
=
−4x
+ 3x − 1 a.) b.) g(x) = −4x − 3x + 10 6
13. Divide: 3
2
4 x + 3x − 2x + 1
x−4
4x + 3x − 2x + 1
14. Divide: x2 + 4
3
2
15. Determine a cubic polynomial function with roots: -­‐3 and 6i. 16. Write the complete linear 3
2
2x
−
5x
− 4x + 3 : factorization of given x+1 is a root. 17. Find all holes and asymptotes: a.) x2 − 1
f (x) = 3
x − x 2 − 4x + 4
4x 3 + 2x + 5
g(x) =
2
b.) 2x − 1 18. A rock is thrown upward from a 300 ft building with an initial velocity of 25 ft/sec. Determine when the rock will hit the ground. Determine the maximum height the rock will go. 19. Write an equation for each statement: a.) The circumference of a circle varies directly with twice the product of its radius, r, and π.
b.) The force of an object varies inversely with its mass, m. 20. The average number of hours of daylight for each month is listed below. Determine a Cubic regression model for the data. Determine the R2 value. Is the regression strong, medium, or weak? Predict the number of hours of daylight when t = 4.5.