Absolute Value Equations & Inequalities
Identify the domain and range of the function: f(x) = |x + 6|
What is domain: All Real Numbers
range: {y| y ≥ 0}
Write the parent function of a linear function.
What is f(x) = x?
Give the vertex and state the domain and range:f(x) = |x| + 3
What is V: (0, 3)
domain: all real numbers
range: {y|y ≥ 3}
Determine whether the function has a minimum or maximum. f(x) = x2 - 8x + 17
What is minimum?
Identify the increasing and/or decreasing intervals of f(x) = -2/3x
What is
Increasing:N/A
Decreasing: (2, inf)
Determine the y values for the following inequality: y ≥ |x| + 2. Draw a table with x and y values.
Hint: You must first find the vertex. Use 7 slots for you table.
What is 5, 4, 3, 2, 3, 4, 5 respectively?
Describe the transformation of the function: f(x) = |x| - 7 and name the parent function.
What is shift down 7, absolute value function?
Give the vertex and state the domain and range: f(x) = 1/3|x| - 7
What is V: (0, -7)
domain: all real numbers
range: {y|y ≥ -7}
Determine the axis of symmetry and vertex of the function: f(x) = 3x2 + 1
What is V: (-1, -4)
A: x = -1
Identify the increasing and/or decreasing intervals: f(x) = -3x2 + 12x - 8
What is
Increasing: (-inf, 2)
Decreasing: (2, inf)
Determine the y values for the following inequality: y < -|x - 4|. Draw a table with x and y values.
Hint: You must first find the vertex. Use 7 slots for you table.
What is -3, -2, -1, 0, -1, -2, -3 respectivley?
Describe the transformation of the function and name the parent function: f(x) = (x - 4)2 + 9
What is right 4 up 9, quadratic function?
Give the vertex and axis of symmetry of the quadratic: f(x) = (x + 1)2 - 8.
What is V: (-1, -8)
A: x = -1
Determine whether the function has a minimum or maximum, the vertex, and the axis of symmetry: f(x)=-2x2 + 8x - 11
What is maximum
V: (2, -3)
A: x = 2
What is the end behavior of the function: f(x) = 2|x + 4|
What is
As x -> inf, f(x) -> inf
As x -> -inf, f(x) -> inf
Identify the domain and range of the function: f(x) = -|2x| + 7
What is domain: all real numbers
range: {y|y ≤ 7}
Describe the transformation of the function and name the parent function: f(x) =1/4(x + 6)2
What is vertical compression by 1/4, left 6, quadratic function?
Give the vertex and axis of symmetry of the quadratic:
f(x) = 1/2x2 - 3
What is V: (0, -3)
A: x = 0
Write the function in vertex form: f(x) = x2 - 12x + 36
What is f(x) = (x - 6)2
Identify the end behavior of the function: f(x) = -x2 + 7
What is
As x -> inf, f(x) -> -inf
As x -> -inf, f(x) -> -inf
Idenitfy the domain and range of the function:
f(x) = { -1 if x ≤ -6
{ -x - 4 if -6 < x ≤ 0
{ |2x - 5| if x > 0
What is domain: all real numbers
range: {y|y ≥ -4}
Write the function for the absolute value parent function where it is reflected on the x-axis, then translated 8 units left and 5 units up.
What is f(x)= -|x + 8| + 5?
Give the vertex and axis of symmetry of the quadratic inequality: y ≤ -1/2(x + 3)2 + 4
What is V: (-3, 4)
A: x = 4
Write the function in vertex form: f(x) = -2x2 + 8x - 1
What is f(x) = -2(x - 2)2 + 7
Idenify the increasing/decreasing intervals and the end behvior of the function: f(x) = -|x + 3| + 6
What is
Increasing: (-inf, -3)
Decreasing: (-3, inf)
End Behavior:
As x -> inf, f(x) -> -inf
As x -> -inf, f(x) -> inf