Key Features Of Graphs
Transformations of Functions
Graphing Functions
Parent Functions
100
Define the term domain
Domain - all possible values of x, reading from left to right.
100
Identify the transformations represented by the letter in the function below.
f(x) = -4(2x + t) -9
t - represents the horizontal shift of t units to the left
100
Given the equation f(x) =x3 - 5x +2
What is the y- intercept(s)
y- intercept - (0, 2)
100
I am the function represented by the equation
y = x2 Who am I
Quadratic Function.
200
Using the diagram below, what are the values of
a) Increasing
b)Decreasing
a) Increasing: (2, infinity)
b) Decreasing: (negative infinity, 2)
200
Write a quadratic function that represents the shift from the parent function, in the diagram below.
right 4 up 2 parent: x2
g(x) = (x - 4)2 + 3
200
Given the equation f(x) = x2 - 8
State the local maximum, local minimum
Local max - N/A
Local Min - (0, -8)
200
I am the function represented by the equation
y = x Who am I
Linear Function
300
Using the diagram below, where is the function
a) positive
b) negative?
a) Positive: (negative infinity, -1) (5, infinity)
b) Negative: (-1, 5)
300
Identify the transformations from the function below.
f(x) = - |x - 4|+ 6
f(x) = - |x - 4|+ 6
- 4: Right Four
+ 6: Up 6
- : Reflected over the x-axis
300
Given the function f(x) = (square root of x) +7
State the End behavior, decreasing and increasing interval
End behavior: as x approach + infinity, f(x) approach + infinity
as x approach 0, f(x) approach 7
Decreasing - N/A
Increasing - (0, + infinity)
300
I am the function represented by the equation
y = x3 Who am I
Cubic function
400
From the graph shown below, identify the following
a) Domain
b) Range
c) Positive Interval?
Domain: [-3, 8]
Range: [-5, 3]
Positive Interval: (-3, 3)
400
Describe how to transform the graph of 'f ' into the graph of 'g'
f(x) = square root of x
g(x) 9 times the square root of x
Vertically stretch the graph of f by the factor of 9.
400
Graph the function f(x) = 2x -8
State;
parent function
domain
range
maximum
x- intercept
Parent function - Linear f(x) = x
Domain - (- infinity, + infinity)
Range - (- infinity, + infinity)
Maximum- N/A
X- intercept - ( 4,0)
400
I am the function represented by the equation
y = -7 Who am I
Constant Function
500
List ALL the key feature of a graph, and define each key feature.
Domain/ Ranges- all x values / all y values
x-int. / y- int. - where graph touch x-axis /y-axis
max/min - highest point, turning point / lowest point, turning point.
+ive /-ive - points of the graph on or above the x axis / parts of the graph on or below the axis.
increasing / decreasing - where the graph is going up / where the graph is going down.
End behavior - the behavior of the graph of f(x) as x approaches - &+ infinity.
500
Given the function f(x) = -2|3x - 9| +2
State the transformation(s) from the parent function.
-: reflected about the x- axis
2: Vertically stretched by a factor of 2
3: horizontally compressed by a factor of 1/3
- 9: shifted 9 units right
+2: shifted 2 units up
500
Given the function f(x) = 1/2 |-4x +2 | -3
State all the key features
Dom - (- infinity , + infinity) Range [-3, + infinity )
xint- (-1,0) (2, 0) yint - (0,-2)
Min ( 0.5, -3) Max - N/A
increasing (0.5, +infinity) Decreasing (-infinity, 0.5)
Neg ( -1, 2) Pos (- infinity , -1) (2, + infinity)
End behavior: x -> infinity, f(x) -> infinity
x -> neg, infinity, f(x) -> infinity
500
I am the function represented by the equation
y = |x| Who am I
Absolute Value Function .