1. Algebra 2/Trigonometry Name: __________________________
Unit 3 Review Date: ___________________________
Directions: Please complete each exercise on a separate piece of paper and follow all directions. NC: Non-Calculator, C: Calculator.
I. Sketch each parent graph in colored pencil and the transformed graph in regular pencil. A window of [-6, 6] for both the x and y-axis should be sufficient for these graphs. (NC)
II. Determine the equation of each transformed graph. (NC)
1) )
a) Quadratic Function
1) y = (x + 2)2 - 5
2) y = ½(x – 1)2
3) A quadratic function that is shifted up 3 and reflected across the x-axis.
3) )
b) Cubic Function
1) y = (x - 4)3 + 1
2) y = -x3 - 2
3) A cubic function that has a vertical stretch by a factor of 2.
c) Absolute Value Function
1) f(x) = -|x| + 2
2) An absolute value function that is shifted to the right 3 units, shifted down 2 units and has a vertical Shrink by a factor of 1/2 .
5) )
d) Reciprocal Function
1) 𝑓 𝑥 = (𝑥−1) −1 −2
2) 𝑓 𝑥 =− 1 𝑥+2
7) )
e) Square Root Function
1) 𝑓 𝑥 =− 𝑥−1
2) A square root function, shifted to the right 3 units, shifted down 2 units and has a vertical stretch by a factor of 3.
9) )
f) Cube Root Function
1) 𝑓 𝑥 =2 3 𝑥 −3
2) 𝑓 𝑥 = 3 𝑥+5 +3

2. III .Do the following: Find the domain and range of each graph; determine if the graph is a function; determine if the inverse of the graph is a function. (C)
IV. Find the equation for the inverse of each function. Then, make a table of values for the function, and graph both the function and its inverse on the same axes. Be sure to show your verification both algebraically (using compositions) and graphically! (C)
V. #1 – 3, evaluate the function at the given value. For #4 – 8, simplify each combination or composition of the functions listed below. (C)
𝑔 𝑥 = 𝑥 2 −3
1) (f + g)(x)
2) (j  h)(x)
3) 𝑗 ℎ (x)
4) (j - f)(x)
6) (h  g)(x)
5) (f + j)(4)
7) (j  g)(x)
8) (h  f)(x)
VI. Graph (NC)