Absolute Value Transformations
What does an a that is in between 0 and 1 do?
Vertical stretch
What are the steps to solve absolute value equations?
1. Isolate 2. Split 3. Solve
"Negate and Flip" this absolute value inequality:
|3x + 4| > -2x + 6
|3x + 4| < 2x - 6
Name the three domain and range notations we have learned.
Inequality notation, set notation, interval notation
What are the steps to formulate a system of equations?
1. Read problem TWICE
2. Identify variables
3. Formulate number sentences
Identify the transformation:
y = 1/3|x + 7| + 6
Vertical stretch by 1/3
Shift left by 7
Shift up by 6
What is the correct order of steps you will take to isolate the absolute value?
4|2x + 8| + 7 = 3x + 18
Subtract 7 on both sides, then divide by 4
Why is it important to graph solutions of absolute value inequalities on a number line?
To see if there is one or two solution sets
When using inequality notation, which inequality symbols do we use for included and not included points?
Included: less than/greater than or equal to
Not included: less than/greater than
Identify the variables of this word problem:
Sally has a total of 126 coins in her piggy bank. The total value of all of her money saved is $32.36. She has a mix of quarters, dimes, and pennies in her piggy bank. She has triple the amount of quarters as she has dimes.
q = quarters
d = dimes
p = pennies
Identify the transformation:
y = 2|x - 2| + 2
Vertical compress by 2
Shift right by 2
Shift up by 2
Solve for x:
|2x + 8| = 8x + 12
x = {-2, -2/3}
Solve the absolute value inequality: |4x + 4|> 2x + 8
x < -2 OR x > 2
When using set notation, what brackets do we use for included and not included points?
Included: [ ]
Not included: ( )
Formulate a systems of equations to represent this word problem:
Sally has a total of 126 coins in her piggy bank. The total value of all of her money saved is $32.36. She has a mix of quarters, dimes, and pennies in her piggy bank. She has triple the amount of quarters as she has dimes.
126 = q + d + p
32.36 = 0.25q + 0.10d + 0.01p
3d = q
Identify the transformation:
y = -10|x - 9| - 5
Reflect across the x axis
Vertical compress by 10
Shift right by 9
Shift down by 5
Solve for x: 3|4x + 7| - 12 = 6x + 3
x = {-2, -1}
Solve for x:
|4x+2|+ 6 < 2x + 12
-4/3 < x < 2
Major League Soccer rules state that soccer balls must be inflated to 13 PSI. If they are inflated any more or less than 0.25 PSI of the desired weight, the ball will be rejected and will be unable to use during the soccer game. Write an absolute value equation that represents the least and most a MLS soccer ball can weigh.
Yeraldi, Gabriel, and Jonathan went to the movie theater together. Yeraldi bought 1 bucket of popcorn, 3 candy bars, and 1 soda for $24.50. Gabriel bought 1 candy bar and 2 sodas for $12.75. Jonathan 1 bucket of popcorn and 5 candy bars for $19.50. Formulate a systems of equations to represent this scenario.
24.50 = 1p + 3c + 1s
12.75 = 1c + 2s
19.50 = 1p + 5c
Identify the transformation:
y = -2/3 |x + 6| - 2
Reflect across the x axis
Vertical stretch
Shift left by 6
Shift down by 2
Solve for x: 5|2x + 4|-10 = -5x + 20
x = {-10, 2/3}
Solve for x:
-3|2x + 5| + 2 < 3x - 10
x < -9 OR x > -1/3
The average starting salary of a teacher at LG Pinkston High School is $30,000. The actual salary can differ by $5,600 depending on the teacher's qualifications. Write an absolute value equation that can represent the maximum and minimum salaries a teacher can make at LGP.
|x - 30,000| = 5,600
Ms. Nogoy is downloading movies, books, and shows on her tablet to keep her occupied on a long flight she is about to take. She downloads a total of 32 pieces of media. She downloads triple the amount of books as she does movies. Movies take up 500MB each, books take up 50MB each, and shows take up 100MB each. The total media downloaded equals 8500MB. Formulate a systems of equations to represent this scenario.
8500 = 500m + 50b + 100s
3m = b