Flashcards
Functions
Cards in this deck (28)
- 1Function/mappinga realtion that uniquely assosiates members of one set with members of another set. Can either be a one one function or a many-one function
- 2one-one functionhas 1 ouput value for each input value and vise versa. For every point y in the range of the funtion, there is only 1 value of x: y=F(x). Graph is a horizontal line that cuts graph once. Normal line
- 3Many-one functionhas 1 ouput value for each input but each ouput value can have more than 1 input value
- 4DomainSet of input values for a function
- 5Rangeset of ouput values for a function
- 6How to find range from domain find domain from rangeput domain into equation of x to get range
find domain from range put in inverse
range on y axix, domain on x - 7composite functionswhen 1 function is followed by another function
- 8what does fg(x) mean?function g acts on x first then f acts on result.
- 9What are the rules for fg(x) like where existsonly exists if hte range of g is contained within the domain of f.
gf(x) doesnt = gf(x) - 10Inverse Functions what domain and ranges = of inverse When does an invesre function exist?The funciton that undoes what f(x) has done. f-1(x)
ff-1(x) = f-1 f(x) =x
Domain of f-1(x) = range of f(x)
Range of f-1(x) = domain of f(x)
inveser only exists with a one-one mapping may have to make a one one by chaning range - 11Self inverse functionwhen f(x) = f-1(x)
- 12how are invesrs graphs relatedreflectiosn of each other int he line y=x. Tue for each one-one function and its inverse. becaue ff-1(x) = x= f-1f(x)
When funciton f is a self-inverse fuctnion, the gprhah of f will be symmetrical about lne y=x - 13Graph of y=f(x)+a is a translation of the graph y=f(x) by the which vector?(0)
(a) - 14Graph of y=f(x-a) is a translation of the graph y=f(x) by the which vector?a
0 - 15Graph of y=f(x-a) + b is a translation of the graph y=f(x) by the which vector?a
b - 16How does y=f(x-a) translate y=f(x)?a units to the right
- 17How does y=f(x+a) translate y=f(x)?a units to the left
- 18How does y=f(x) - a translate y=f(x)?a units down
- 19How does y=f(x) +a translate y=f(x)?a units up
- 20What is the graph of y=-f(x)?refleciton of the graph of y=f(x) in x-axis
- 21What is the graph of y=f(-x)?reflection of hte graph of y=f(x) in y-axis
- 22What is the graph of y=af(x)? whatn happends if negative?a stretch of the graph y=f(x) with the stretch factor a parallel to the y-axis
Note: if a<0 then y=af(x) can be considered a stretcy of y=f(x) with a negtative scale factor or as a stretch with a positive scale factor followed by a feflection in the x-axis - 23What is the graph y=f(ax)stretch of the graph y=f(x) with stretch factor 1/a parallel to x-axis
- 24What are the vertical transformations?y=f(x) +a transalation 0 a
y=-f(x) reflection in x-axis
y=af(x) vertical stretch, factor a - 25What are the horizontal transformations?y=f(x+a) translation -a 0
y=f(-x) reflection in y-axis
y=f(ax) horizontal stretch, facotr 1/a - 26Does order matter: When one horizontal nad one vertical translation are combined? When 2 horizontal or 2 vertical translation combined?no
yes - 27Do vertical and horizontal transformations follow the normal order of operations?Vertical yes
horizontal follow opposite order to normal operations - 28what does tranlsation of 4 0 mean? What does horizontal factor 1/2 mean?replace x by x-4 = y=x-4
means replace x by 2x y =2x-4
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- A Level A Level Maths (Pure Maths 1) Flashcards on Functions, created by HRYN red on 13/04/2022.
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- HRYN red
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