1. Determine analytically if the following functions are even, odd, or neither.
a. f(x) = 5x 3 – 2x b. f(x) = x 2 + 3x – 2
2. Suppose (1, -2) is on the graph of y = f(x). Find a point on the graph of the transformed function y = f(x + 5).
3. Let f(x) = . Find a formula for a function g whose graph is obtained from f by the given sequence of transformations.
(1) shift left 3 units
(2) vertical stretch by a factor of 2
(3) reflect across the x-axis
4. Find the slope-intercept form of the line which passes through the points P(-1,0) and Q(-4,6).
5. A plumber charges $80 for a service call plus $30 per hour.
a. Find a linear function that represents the total daily charges C, in dollars, as a function of the time t, in hours, spent at a given location.
b. If the total charge was $140, how many hours did he work?
6. Find the equation of the line passing through the point (-3, 5) and perpendicular to the line y = x – 7.
7. Find the equation of a line parallel to x = 7 and passing through the point (2, -5).
8. Find the average rate of change of the function f(x) = x 2 + 5x + 1 over the interval
[-2, 1].
