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Functions - Coggle Diagram
Functions
Surjective
surjective - every element of the codomain has at least one
element of the domain
no element in the codomain is unused ,
horizontal line test - if the function is surjective , then every
horizontal line drawn must intersect the graph at least once
Sketching Graphs
cubic functions - general function is ax3 + bx2 +cx +d which
generally consists of a smooth curve with two turning points
when a is greater than 0 the graph is rising from left to righ
when a is less than 0 the graph is falling from left to right
example - y = x(x+1)(x-2)
1) y = x3 - x2 - 2x , multiply brackets out
2) let y = 0 , (x+0)(x+1)(x-2) = 0 , x = 0 . x=-1, x=2. the curve
crosses the x axis at (0,0) , (-1,0) , (2,0)
3) let x = 0 to solve y , y= 0 - 0 - 2(0) , the line crosses the y axis
at the point (0,0)
linear - the graph of a linear function can be found by find the points that intersects the x and y axis
example - y = 2x -4
let y = 0 , 2x - 4 = 0 , x = 2
let x =0 , y = 2(0) - 4 , y =-4
points are (0,-4) and (2,0)
quadratic - general form of a quadratic function is ax2 + bx +c where a,b,c are constants and a is not = to 0
when a is greater than 0 the graph would be a u shape
lowest point on the curve = minimum point
when is is less then 0 the graph would be a n type shape
highest point on curve is maximum point
Injective
injective functions - a function is said to be injective if every output in b has a unique input in a
it is not necessary that every element in the codomain has acorresponding element in the domain
horizontal line test - if it crosses the line at most once then it
is said to be injective
Bijective
a function is bijective if for every element in the b has an
exactly 1 element in a such that f(x) = y
bijective function is both surjective and injective