Equations
Inequalities
Characteristics
Transformations
Miscellaneous
100
|4p−7|=3
4p−7=−3 or 4p−7=3
100
|4t+9|<3
−3<4t+9 < 3
100
What is the equation of the graph above
f(x ) = -I x + 4 I + 2
100
Describe the transformation of the equation below from the parent function of y = IxI
y = I x + 2 I - 5
Left 2 down 5
100
You left your wallet in your car. A friend is texting you to go to the movies. You will need $12.95 for a ticket. You think you have $20 in your wallet, give or take $5. Write and solve an absolute value inequality representing the possible amount of money in your wallet. Can you afford to go to the movie?
The amount of money, x, in your wallet is: $15 < x < $25.
You can afford to go to the movie.
200
|2−4x|=1
2−4x=−1 or 2−4x=1
200
|6−5x|≤10
−10≤6−5x ≤ 10
200
What is the equation of the graph below?
f(x)= -|x|+1
200
Y= |x-1| +5
right 1, up 5
200
You are asked to buy some small decorative pumpkins to bring to a Halloween party. The small pumpkins are sold in bags listing the weight as 1.2 pounds. The clerk tells you the weight varies by less than 0.15 pounds. Write and solve an absolute value inequality representing the possible range of weights of the bags of pumpkins.
The weight, x, will be
1.05 lbs < x < 1.35 lbs
300
6u=|1+3u|
1+3u=−6u or 1+3u=6u
300
|12x+1|≤−9
There is no solution to this inequality.
300
What is the range of the absolute value function?
[0, infinity)
300
Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9
Left 4 Down 9
300
∣x+2x∣=15
x+2x=−15 or x2+2x=15
400
|2x−3|=4−x
2x−3=−(4−x)=x−4 or 2x−3=4−x
400
|2w−1|<1
−1<2w − 1<1
400
What is the vertex of the following function?
y= -4|x+2|+5
(-2,5)
400
Describe the transformation from the Absolute Value Parent Function.
f(x)=1/5|x|-4
Compresses wider, shifts down 4 units
400
The recommended temperature for serving hot cream soups is 195º F. plus or minus 5 degrees. Write and solve an absolute value equation representing the maximum and minimum serving temperatures for hot cream soup.
minimum temp. is 190º F.
maximum temp. is 200º F.
500
∣1/2z+4|=|4z−6|
1/2z+4=−(4z−6)=6−4z or 1/2z+4=4z−6
500
|2z−7|>1|2z−7|>1
2z−7<−1 or 2z−7>1
500
What is the vertex of the following function?
y= 4|x|+1
(0,1)
500
Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units
f(x)=2|x-1|-9
500
The specifications for the manufacture of a ball bearing requires a diameter of 3.52 cm with an allowable margin of error of at most 0.05 cm. Write and solve an absolute value equation representing the maximum and minimum allowable diameter.
minimum diameter is 3.47 cm.
maximum diameter is 3.57 cm.