**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].

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