Functions and their transformation

COMPILED BY: MOAKAMEDI MOJAKI CHARLES
(FOUNDER OF ARDEN TUTORIAL)




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,TABLE OF CONTENT(S)

1. UNDERSTANDING FUNCTION……………………………page 3

2. LINEAR FUNCTION WITH POSITIVE SLOPE………page 18

3. LINEAR FUNCTION WITH NEGATIVE SLOPE …..page 36

4. POSITIVE AND NEGATIVE PARABOLA……………..page 44

5. HYPERBOLIC FUNCTION…….….……………………………page 74

6. EXPONENTIAL FUNCTION….……………………………….page 132

7. MIXED POBLEMS……………………………………………………page 151




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, 1. Understanding function

Function is a relationship or rule between two sets, the domain (x) and the range (y) in
the equation where for every value of x there is one specific value of y.




TYPES OF FUNCTIONS




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, TRANSLATION
REFLECTION OF COORDINATES



REFLECTION ABOUT AXIS




Figure a: Reflection about y-axis Figure b: Reflection about x-axis

Given (X; Y) as coordinates to be reflected about Y-axis (line Y).
If the blue arrow is revolved slightly clockwise or anti-clockwise as indicated in figure a, it will end up
on the negative side of x-axis. This is a reflection of a point about y-axis, (X; Y) become (-X; Y).
Reflection about y-axis affects x-coordinate.

If the blue arrow is revolved slightly clockwise or anti-clockwise as indicated in figure b, it will end up
on the negative side of y-axis. This is a reflection of a point about x-axis, (X; Y) become (X; -Y).
Reflection about x-axis affects y-coordinate.

EXAMPLES ON REFLECTING POINTS ABOUT X-AXIS

1. A (2; 5)
2. B (-1; 3)
3. C (-3; -3)
4. D (6; -1)

SOLUTIONS
(X; Y) => (X; -Y)

1. A(2; 5) => A’(2; -5)
2. B(-1; 3) => B’(-1; -3)
3. C(-3; -3) => C’[-3; -(-3)] => C’(-3; +3)
4. D(6; -1) => D’[6; -(-1)] => D’(6; +1)



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