Advanced Functions 1.1

Question 1

relation

Answer 1

any set of points which connect two variables

ex. {(1,2),(0,3)}

Question 2

function

Answer 2

a relation in which there is a single, unique output for each input

Question 3

domain/range

Answer 3

the set of all x/y-values for a given relation

Question 4

interval of increase/decrease

Answer 4

the domain of a function for which f(x) is increasing/decreasing from L to R

Question 5

even function

Answer 5

a function for which f(-x)=f(x) for all x in the domain of f, symmetric over y-axis

Question 6

odd function

Answer 6

a function for which f(-x)=-f(x) for all x in the domain of f, symmetric about the origin

Question 7

continuous function

Answer 7

for every value c in the domain, f(c) is defined, and as x->c, f(x)->f(c)

Question 8

discontinuity

Answer 8

the point at which a function is not continuous (ie. a break in the graph of a function)

Question 9

vertical test

Answer 9

a visual test to determine if a relation is a function

Question 10

absolute value

Answer 10

the magnitude of a real number, without regard to its sign

Question 11

inverse function

Answer 11

the inverse f-1(x) of f(x) is the function for which f(f-1(x)) = x and f-1(f(x))

Question 12

symmetrical about the origin

Answer 12

unchanged when reflected across both the x and y axis

Question 13

cubic

Answer 13

starts in the 3rd quadrant and ends in 1st

Question 14

logarithmic

Answer 14

only exists to the left of the y axis. inverse of exponential.

Question 15

root

Answer 15

only exists in the 1st quadrant, looks like a plateau

Question 16

reciprocal

Answer 16

two lines, two asymptotes

Question 17

end behaviours of a root function

Answer 17

as x->infinity, y->infinity. as x->0, y->0.

Question 18

end behaviours of a reciprocal function

Answer 18

as x->infinity, y->0. as x->-infinity, y->0.