Operations with Functions
Inverse Functions
Absolute Value Inequalities
Absolute Value Functions
Interval Notation
Find the Inverse
100
If f(x) = x + 2 and g(x) = 2x - 4, what is f(x) + g(x) ?
What is 3x - 2
100
If f = (3, 2), (-2, 3), what if f^-1(x)?
What is f^-1(x) = (2, 3), (3, -2)
100
What is the difference between open circle and close circle for the solutions of an inequality?
Open circle means the number is not a solution
Close circle means the number is a solution
or
Open = not included
Close = included
100
What is the parent function to all absolute value functions?
f(x) = |x|
100
Write the following inequality in interval notation
x < 8
(-∞, 8)
100
Find the inverse of this function:
h(x)=3/(-x-2)
h^-1(x)=-3/2 x-2
200
If f(x) = 2x and g(x) = -x - 4, what is f(x) - g(x) ?
What is 3x + 4
200
Explain how you would find the inverse of a function algebraically.
What is First, you swap x and y and then solve for y.
200
Is -4 a solution to the following inequality:
|2x+7| > 1
What is the cube root of -81?
not a solution
200
Identify and describe the transformation:
g(x) = |x| + 4
Vertical translation of four up
200
Look at the Graph. Write the inequality in interval notation.
[-4, -1)
200
Find the inverse of this function:
f(x)=2/7 x-10/7
f^-1(x)=7/2 x+5
300
If f(x) = x + 1 and g(x) = x + 3, find f(g(x))
What is x + 4
300
An inverse and its function are _________________of each other graphically.
What is reflections
300
Solve the following inequality:
|x+4| < 2
x < -2 and x > -6
300
Describe the transformation:
Horizontal Shift Left 4
Vertical Shift Up 3
300
Write the following in interval notation
x < 3 or x ≥ 5
(-∞, 3) or [5, ∞)
300
Find the inverse of this function:
g(x)=-2x+5
g^-1(x)=-1/2x+5/2
400
If f(x) = 2x - 4 and g(x) = 3x - 5, what is g(f(5))?
What is 13
400
An inverse and its function are reflections of each other over the line y = _____
What is x
400
Solve and graph the inequality:
4|2x-1|-2 > 10
x > 2 or x < -1
400
Identify and describe the transformation:
h(x) = 0.5|x-3| + 1
Vertical compression by 0.5
Horizontal Shift Right 3
Vertical Shift Up 1
400
Look at the picture. Which number line corresponds to [-2, 5]?
Graph 4
400
Find the inverse of this function:
h(x)=1/x-1
h^-1(x)=1/(x+1)
500
If f(x) = 3x - 1 and g(x) = 4x + 7, if you calculate f(x) / g(x), what can x not be in this operation?
What is -7/4
500
How would you verify the two functions are inverses of each other by using a composition of functions?
What is by showing that f(g(x)) and g(f(x)) both equal x.
500
Solve and graph the inequality:
-2|x+1| > 3
Only extraneous solutions
500
Describe the transformation:
Vertical Reflection across x-axis
Horizontal Shift Right 2
Vertical Shift Down 1
Vertical stretch by a factor of 2
500
Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?
Graph 1
500
Find the inverse of this function:
f(x)=- 3/(-x-2)-2
f^-1(x)=3/(x+2)-3