Name________________________
Date ________
Algebra 2 HW: Introducing Absolute Value
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
I. REVIEW – Evaluate the expression when x = -.75
(1 pt each)
1.
x  .25
2.
x  .75
3.
x  .25
4.
x  .75
x  1  .25
5.
II. PRACTICE – 5 pt each
Sketch the graph and identify the characteristics of the graph.
1. y  x  2  4
2. y   x  3
Domain:
Domain:
Range:
Range:
Vertex:
Vertex:
y-intercept:
y-intercept:
zeros (roots, x-intercepts, solutions):
zeros (roots, x-intercepts, solutions):
Increasing:
Increasing:
Decreasing:
Decreasing:
End Behavior:
End Behavior:
Slope of right branch:
Slope of right branch:
3.
y
1
x  4 1
2
4.
y   x 3  2
Domain:
Domain:
Range:
Range:
Vertex:
Vertex:
y-intercept:
y-intercept:
zeros (roots, x-intercepts, solutions):
zeros (roots, x-intercepts, solutions):
Increasing:
Increasing:
Decreasing:
Decreasing:
End Behavior:
End Behavior:
Slope of right branch:
Slope of right branch:
IV. REACH FOR THE STARS! – 4 pts each
Sketch an absolute value function whose vertex is at (0,2) such that as x->∞, f(x) x->∞, and as
x->-∞, f(x) x->∞. Discuss the zeros of this function.
Name________________________
Date ________
Algebra 2 HW: Transformations with Absolute Value
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
25
I. REVIEW – complete all of these (1 pt each)
1.
3.
x3  x 4 =
4
2. 2 x  3 x
x3
x4
6 x3
4.
24 x 4
5. Explain the exponent rules for multiplying and dividing exponents with like bases.
II. PRACTICE – 2 pt each
Graph the following and specify the NEW vertex.
6.
y  x Vertex
7.
y
y  x 1
y
1
x
2
8.
y
x
9.
Vertex
Vertex
y
y
x
10.
y  2x
Vertex
y
x
y  x  1 Vertex
x
11.
y  x 1
Vertex
y
x
x
12.
y  x 2
Vertex
13.
y
yx
Vertex
14.
y   x 1
Vertex
y
y
x
x
x
III. MORE PRACTICE – 4 pt each
15. y  3 x  1  4
Vertex
16. y   x  2  5
y
Vertex
17. y  
IV. REACH FOR THE STARS: Write the equation
18.
19.
Vertex
y
y
x
1
x3 4
2
x
x
Name________________________
Date ________
Algebra 2 HW: Absolute Value Equations
Complete the 5 review questions and then choose 20 POINTS worth of new material. ______
25
Mix and match as YOU NEED to feel confident with this material.
I. REVIEW – complete all of these (1 pt each)
Simplify.
1.
4.
25
3 12
2.
3.
50
5.
12
5  20
II. PRACTICE – 2 pt each
Solve the following over the REAL numbers. Remember to check for extraneous solutions. Show
and solve both derived equations.
6. |x - 3| = 10
7. |x + 2| = 7
8. |x - 10| = -20
9. |3x - 2| = 13
10. |2x + 5| = 3x
11. |3d - 4| = 14
III. MORE PRACTICE – 3 pts each
Solve the following over the REAL numbers. Remember to check for extraneous solutions. Show
and solve both derived equations.
12. |5x - 10| + 5 = 45
13. 2|3x + 1| - 5 = −3
14. 2|2d - 5| - 3 = 23
15. −3|x + 24| = −7x
16. -3|x + 8| - 1 = -22
17. |10 – 7g| = 2g
IV. REACH FOR THE STARS! – 4 pts each
Solve the following equations. “No solution” and “All Real Numbers” are valid answers.
18. |f + 3| = 2f + 4
19. |2x + 4| = |x|
(You can do this one! Think about it!)
Name________________________
Date ________
Algebra 2 HW: Absolute Value Inequalities
Complete the 5 review questions and then choose 20 POINTS worth of new material. ______
25
Mix and match as YOU NEED to feel confident with this material.
I. REVIEW – Simplify or solve over the complex numbers (1 pt each)
1.
4.
34 3
34 5
2.
2 4 8
5.
2 8
II. PRACTICE – 2 pt each Solve for x. Then graph the solution.
6. -5x – 6 < 19
7. 5 ≤ 2x + 3 ‹ 11
8. |3x + 4| ≥ 2
9. |2x + 1| ‹ 7
10. |4x + 2| ≥ 8
3.
16  2 81
III. MORE PRACTICE – 3 pts each
11. 2x ‹ 10 or
x
3
2
12. 3 
p
0
2
2
x5  5
3
14. 2|5 + 2x| - 7 ≥ 15
15. 3x  4  3  5
16. 3 4 x  7 12   3
13.
IV. REACH FOR THE STARS! – 4 pts each
Solve and graph the following inequalities.
17.
2x  1  7   2
18. -½ |3x + 2| - 1 < -5