Name:____________________________________________ Algebra Boot Camp Part 1

Parent Functions:

1.) Describe in your own words what a function is.

2.) A list of parent functions is given below. Write the equation for the functions, graph the function in the grids, and identify the key characteristics about the graphs’ shapes.

a. Quadratic b. Cubic c. Square rootf(x) = f(x) = f(x) =

d. Absolute value e. Inverse f(x) = f(x) =

3.) Explain what the following transformations do to a parent functiona. f(x- a) b. f(x) + b

b. –f(x) d. f(-x)

4.) Graph f(x) = (x – 3)2 + 2 5.) Graph g(x) = 1−|x+3| 6.) Graph h(x)= −√ x−4

Multiplying and Dividing Polynomials

1.) Define in your own words what a polynomial is.

2.) Perform multiplication on the following polynomials:a. (x + 1)(x – 1) b.) (3y – 5)2

c. (√ x−4 ) (√ x+4 ) d.) (x+4)2

e. (√ x+2−2 ) (√ x+2+2 ) f.) (x+2)3

3.) Write down any observations you had about 3a-f.

4.) Solve the following problems using division of polynomials. (Hint: You can use long division of polynomials or synthetic division; I would try both, but that’s just me… because review is awesome; you can’t get enough of it)

a.

x3+6 x2+12 x+8x+2 = ? b. (x – 2)( ?) = x3 – 8