Function Composition
Parent Functions
Domain and Range
Functional Inverses
100
Function Composition
f(x) = x + 2
g(x) = 4x
f(g(x))
f(x) = x + 2
g(x) = 4x
f(g(x))
What is 4x + 2?
100
Parent Functions
The rule for the parent cubic function.
(Write the expression)
The rule for the parent cubic function.
(Write the expression)
What is x3?
100
Domain and Range
One of the following statements is correct.
A domain is all the values that can be:
A) Results from a function
B) Intercepts in a function’s graph
C) Put into a function
One of the following statements is correct.
A domain is all the values that can be:
A) Results from a function
B) Intercepts in a function’s graph
C) Put into a function
What is C) Put into a function?
100
Inverse Functions
What inverse functions do.
What inverse functions do.
What is swap inputs and outputs?
200
Function Composition
f(x) = 2x – 3
g(x) = x + 1
f(g(x))
f(x) = 2x – 3
g(x) = x + 1
f(g(x))
What is 2x – 1?
200
Parent Functions
A function family that has a vertex.
A function family that has a vertex.
What is quadratic/absolute value?
200
Domain and Range
One of the following statements is incorrect.
A range represents:
A) Result from a function
B) The collection of outputs
C) “y” values on a graph
D) None of these are incorrect
One of the following statements is incorrect.
A range represents:
A) Result from a function
B) The collection of outputs
C) “y” values on a graph
D) None of these are incorrect
What is D) None of these are incorrect?
200
Inverse Functions
The inverse of the cube root function.
The inverse of the cube root function.
What is the cubic function?
300
Function Composition
f(x) = 3x + 2
g(x) = 2x2
f(g(x))
f(x) = 3x + 2
g(x) = 2x2
f(g(x))
What is 6x2 + 2?
300
Parent Functions
A function family that has degree of 1?
a linear function
300
Domain and Range
The domain of this function:
f(x) = x2 - x + 12
All Real Numbers
300
Inverse Functions
The reason the inverse of the points below is not a function:
(1, 4), (-3, 5), (2, 4), (1, 4)
There is more than one output for the input of 4.
400
Function Composition
f(x) = 3x + 2
g(x) = x2
g(f(x))
f(x) = 3x + 2
g(x) = x2
g(f(x))
What is 9x2 + 12x + 4
400
What is the vertex of the parent function of the quadratic function?
(0,0)
400
Domain and Range
The range of this function:
f(x)=sqrt(x)+3
greater than and equal to 3
400
Inverse Functions
The inverse function for x2 + 3.
The inverse function for x2 + 3.
What is the square root of the quantity (x – 3)?
500
Function Composition
f(x) = x + 1
g(x) = 2x
h(x) = x2
f(g(h(x)))
f(x) = x + 1
g(x) = 2x
h(x) = x2
f(g(h(x)))
What is 2x2+1?
500
Parent Functions
Stand up and make the graph of the absolute value with your arms!
Stand up and make the graph of the absolute value with your arms!
What is
?
? 500
Domain and Range
The range of this function:
y=-2
500
Inverse Functions
The equation for the line that inverse functions reflect across.
The equation for the line that inverse functions reflect across.
What is y = x?