Key Features Of Graphs
Transformations of Functions
Graphing Functions
Parent Functions
100
What is the domain of a given function
Domain - all possible values of x, reading from left to right.
100
Identify the transformations represented by the letters in the function below.
f(x) = -4(x + t) -9
t - represents the horizontal shift of t units to the left
100
Given the equation f(x) =x3 - 5x +2.
State 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
Where is the functions increasing and decreasing?
Increasing: (2, infinity)
Decreasing: (neg. infinity, 2)
200
Write a quadratic function to model this shift from the parent function.
f(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
Where is the function positive or negative?
Positive: (neg. infinity, -1) (5, infinity)
Negative: (-1, 5)
300
Name the transformations of the following function:
f(x) = - |x - 4|+ 6
Right Four
Up 6
Reflected over the x-axis
300
Given the function f(x) = (square 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
What is the Domain, Range, and 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 of x
Vertically stretch the graph of f by the factor of 9.
400
Graph the function f(x) = (2x -8)
State the 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
state and define all key features of a given graph
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 from the parent function.
reflected about the x- axis
Vertically stretched by a factor of 2
horizontally compressed by a factor of 1/3
shifted 9 units right
shifted 2 units up
500
Given the function f(x) = 1/2 |-4x +2 | -3
State 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)
500
I am the function represented by the equation
y = |x| Who am I
Absolute Value Function .