(1) for the Following Function

Key, 1.1

(1) For the following function:

(a) What is

(b) For what x-values is at the x-intercepts, x = 3 and x = -3

Find the two points on f at x = 1: (1, - 8) and (3, 0).

Find the slope of the line containing them: , then pick a point (I’m going with (3, 0) ), and use point-slope form (go ahead and solve for y, too)

(2) Give the average velocity of an object moving along the curve between x = 1 and x = 4.

(3) A test tube is knocked off a tower at the top of a green building. (For the purposes of this experiment the tower is 400 feet above the ground. It’s height after t seconds is .

a) the average speed in the first two seconds of the fall (tip: that’s t = 0 to t = 2).

b) the average speed in the last two seconds of the fall (tip: you must first find the time when said object hits the ground, and count back two seconds).

Hits ground when

So the last two seconds would be between t = 3 and t = 5.

(4) Find the difference quotient of the function:

(a)

(b) (tip: )

(5) Graph the piecewise function:

Yours probably won’t look as spectacular as this:

(6) Let’s say I define a piecewise function

What would the value a have to be for the two pieces to ‘connect’, so that there was no jump in the function?

Soln: The only place where the function could have a jump is at the point where the domain ‘splits’, at x = 1. The two pieces would have to be equal there. So plug 1 into both of them, and solve the equation for a:

(7) Graph the following translates of elementary functions:

(a) Shift root x up 2: (b) inverts, then up 4:

(I don’t really like this graph – stupid computer)

(8) Use the unit circle or standard triangles to evaluate the following:

(a)

(b)

(d)