Download Chapter 1 Study Guide - Liberty Union High School District

Chapter 1 Study Guide
Algebra II
1.1 Parent Functions & Transformations
Graph the function and its parent function. Then describe the transformation.
1)
m(x) = 2x
2)
n(x) = │x + 4│
y
y
y
4
4
3
3
3
2
1
2
1
1
x
1.2 Transformation of Linear &
Absolute Value Functions
Absolute Value Equations & Inequalities
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
2
3
4
Write a function g whose graph represents the indicated transformation of the graph of f
1)
f(x) = x ; translation of 3 units down and horizontal stretch by a factor of 2
2)
f(x) = │x│; reflection on the x-axis followed by a translation of 5 units to the left.
Solve and graph the solution set
1)
1.3 Modeling with Linear Functions
-3
f (x) = 1/3x2 +1
4
2
-4
3)
│4 + x│ ≥ 7
2)
│3x – 2│< 8
3)
│-5x│+ 1 = 16
Write a Linear Equation and interpret the slope and the y-intercept
1)
2)
# of people, x
Gallons of water, y
1 3 5 7
4 7 10 13
3) Suppose you receive $100 for a graduation present, and
you deposit it in a savings account. Then each week
thereafter, you add $5 to the account but no interest is
earned. The amount in the account is a function of the
number of weeks that have passed.
Solving Two Linear Systems
Solve the system
1)
1.4 Solving Linear Systems
4x + 15y = 17
x – 5y = 13
2)
3y – 2x = 18
6y = 4x + 24
3)
2x – 12 = 8y
3x – 12y = 36
Solve the system
1)
x+y–z=4
2x + 3y + z = 7
x – 2y + 3z = -6
2)
x + 2y + 4z = 3
4x – 2y – 6z = 2
2x – y – 3z = 1