Domain & Range
y values
Describe the transformation of the parent function f(x)=∣x∣.
f(x)= |x|+2
up 2
Solve for all values of b in simplest form.
|9b|= 9
b= -1 , 1
Will the answer to |ax|>b look like
a) >x>
b) x< or x>
b) x< or x>
A room’s temperature is exactly 4°F away from the target temperature of 72°F. Write an absolute value equation that represents the possible room temperatures.
∣t−72∣ = 4
What is the range of the function f(x)=|x|?
y≥ 0
or
[0,∞ )
Describe the transformation of the parent function f(x)=∣x∣.
f(x)= |x-4|-8
right 4, down 8
Solve for all values of y in simplest form.
32= |y+5|
y= -37 , 27
Solve the following inequality algebraically.
∣x−4∣ > 12
x< -8 or x> 16
A cereal box should weigh 18 ounces, but its actual weight may be within 0.5 ounce of the target weight. Write an absolute value inequality representing the acceptable weights.
∣w−18∣ ≤ 0.5
Find the range of the given function.
f(x)=|x+12| +8
[8,∞ )
or
y>= 8
Write the equation of a function g(x) which would shift the parent function f(x)=|x| down 4 units and left 5 units.
g(x)=|x+5|-4
Solve for all values of x in simplest form.
|2-2x| +1 = 7
x= -2 , 4
Solve the following inequality algebraically.
∣x+8∣ < 5
-13 < x < -3
A student’s score was exactly 7 points away from the class average of 82. Write and solve an absolute value equation to find the student’s possible scores.
|s−82| = 7
s=75 or s=89
Find the range of the function
f(x)=∣x−3∣−3
[-3,∞ )
or
y>= -3
The graph of f(x)=∣x∣ is given. Write the equation of a function h(x) which would reflect the graph over the x-axis then right 5 units.
h(x)= -|x-5|
Solve the equation for all values of x.
|x-2| -6 = 3x
x = -1
Solve the following inequality algebraically.
5|x−9|−3 > 12
x<6 or x>12
A machine fills bottles with 20 ounces of juice. A bottle is accepted if its actual amount is within 1.5 ounces of 20 ounces. Write and solve an absolute value inequality to find the acceptable amounts.
∣x−20∣ ≤ 1.5
18.5 ≤ x ≤ 21.5
Find the range of the given function.
f(x)=−∣3x+12∣+5
(-∞ ,5]
or
y<=5
The graph of f(x)=∣x∣ is given. Write the equation of a function h(x) which would first stretch the graph vertically by a factor of 3 then shift it to the left 4 units and up 2 units.
h(x)= 3|x+4|+2
Solve for all values of xx in simplest form.
8 + 3|4x+10| = 29
x= -3/4 , -17/4
Solve the following inequality algebraically.
4|x+10| + 2 ≤ 10
−12 ≤ x ≤ −8
You, a school, and a friend’s house are located along the same straight road. The school is 8 blocks from your house. Your friend lives 3 blocks from the school, but you do not know whether the friend lives closer to your house or farther away. Write and solve an absolute value equation to find the possible distances between your house and your friend’s house.
|x−8|=3
x=5 or x=11