ABS VAL Equations
Solve the equation
|1 - 2/3x| = 9.
What is x = -12 and x = 15.
5 - 9| 9 - k| > -13
What is 7 < k < 11
Describe the transformations from the parent absolute value function.
y=2abs(x-2)-4
Vertically Stretched by 2, Translated Right 2 & Down 4
Which reflection will impact the range of an absolute value function?
Vertical Reflection
What has roots as nobody sees,
Is taller than trees,
Up, up it goes,
And yet never grows?
Mountain
Solve the equation
|x - 2| + 6 = 0.
What is you cannot solve, therefore no solution.
4| 8x - 2 | - 5 < 19
What is -1/2 < x < 1
Describe the transformations from the parent absolute value function.
y=-1/3abs(x)+5
Reflected Down, Vertically Compressed by 1/3, Translated Up 5
Give the domain, range, vertex, and axis of symmetry for
f(x)=abs(2x+5)-3
V: (-2.5,-3) D: R
AoS: x = -2.5 R: y >= -3
Voiceless it cries,
Wingless flutters,
Toothless bites,
Mouthless mutters.
Solve the equation
|x + 3| - 1 = 0.
What is x = -2 and x = -4.
2| 8k - 10 | - 1 > 75
What is k > 6 or k < -3.5
Without graphing, identify the vertex and axis of symmetry from the parent absolute value function.
y=2abs(x-2)+3
Vertex: (2, 3)
AoS: x = 2
Find the vertex and intercepts
f(x)=2abs(x+3)-6
V: (-3,-6)
x-int: (-6,0) & (0,0)
y-int: (0,0)
It cannot be seen, cannot be felt,
Cannot be heard, cannot be smelt.
It lies behind stars and under hills,
And empty holes it fills.
It comes out first and follows after,
Ends life, kills laughter.
Darkness
Solve the equation
|3x - 2| = x.
What is x = 1 and x = 0.5.
10| 4x – 1 | - 7 ≤ 103
What is -2.5 ≤ x ≤ 3
Without graphing, identify the vertex and axis of symmetry from the parent absolute value function.
y=-1/2abs(x)-2
Vertex: (0,-2)
AoS: x = 0
Find the Max/Min
f(x)=-|x-2| on [-2, 3]
Max: 0
Min: -4
Alive without breath,
As cold as death;
Never thirsty, ever drinking,
All in mail never clinking.
Fish
Write an absolute value equation that has the given solutions: 3 and 9.
|x - 6| = 3.
1 – 3| -9n – 10 | ≥ -2
What is -11/9 ≤ x ≤ -1
Describe the transformations of
-5abs(-2(2x-6))-7+3
Vertical Reflection over x, Vertical Stretch by 5, Horizontal Reflection over y, Horizontal Compression by 1/4, Horizontal Translation Right 3, Vertical Translation Down 4
BONUS: What is the vertex of the following absolute value function?
y=abs(3x-6)
Vertex: (2,0)
This thing all things devours;
Birds, beasts, trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slays king, ruins town,
And beats mountain down.
Time