Describing
Function notation
?
Even, Odd, Neither
Vocab
100
Describe the transformation expressed by
f(x) - 9
Translated 9 units to the down.
100
Express g in terms of f if the graph of f is translated 5 unit up
g(x) = f(x) + 5
100
Does f(x) represent the input or the output?
The output of function f
100
A graph is even when
It is symmetrical over the y-axis/a reflection over the y axis produces the same the graph
100
Shifting the graph is referred to as a
Translation, Translating
200
Describe the transformation expressed by
f(x -3)
Translated 3 units to the right
200
Express g in terms of f if the graph of f is translated 8 unit left
g(x) = f(x+8)
200
How does scaling the inputs of a function by 4 transform its graph?
It would compress it horizontally by a factor of 1/4.
200
Is this graph even, odd, or neither?
This graph is neither.
200
Mirroring the graph over an axis is referred to as
Reflection, Reflecting
300
Describe the transformation expressed by f(x+5)+7
Translated 5 units to the left and 7 unit up.
300
Express g in terms of f if the graph of f is translated 4 unit down and 1 unit right
g(x) = f(x-1) -4
300
If f(t) represents the height on a Ferris wheel, and a different wheel can be modeled by h(t) = 6f(3t).
How does the height and speed of the spinning wheel modeled by function h compare to the wheel for f?
Wheel h is 6 times taller and spins 3 times faster than f.
300
What is true about the inputs and outputs of odd functions
Opposite inputs Produce opposite outputs
f(x) = -f(-x)
300
Scaling a function horizontally changes the
Inputs
400
Describe the transformation expressed by
-f(-x+7)
Translated 7 units to the left and reflected over both axes.
400
Express g in terms of f if the graph of f is translated 2 unit up and 3 unit right, then reflected over the x axis.
g(x) = -f(x-3) + 2
400
True or false: all transformations keep the original size and shape of the function
False. When we scale the inputs or outputs, it changes the size or shape
400
Which of these graphs is odd
none, they are all even
400
Scaling the function vertically changes the_______. The types are __________ or ____________
Outputs, Compress/Squashed or Stretched
500
Describe the following transformation expressed by
f(-5x-3)+9
The graph of f is translated right 3 units and up 9 units, reflected over the y-axis and compressed horizontally by a factor of 1/5
500
Express g in terms of f if the graph of f is translated 10 units down and 6 units left, reflected over the x-axis and stretched vertically by a factor of 3.
g(x) = -3f(x + 6) - 10
500
A bridge is built in the shape of a parabolic arch.
The bridge has a span of 50 meters and a maximum height of 40 meters. How do you modify f(x)=x(50-x) so it models the height of the bridge?
f(x) = (40/625)x(50 - x)
500
Function f has the following points (-1, 2), (0,0), (1,4) is the function even odd or neither?
The function is neither.
If it was odd then it would have the points (-1, 2) and (1, -2) or (1, 4) and (-1, -4).
If it was even then it would have the points (-1, 2) and (1, 2) or (1, 4) and (-1, 4).
500
m(x)=-m(-x) is true when the function is ________
odd