Math Transformations

*g(x)=(5x^2+2)/(6x−6) −g(x)

(- 5 x^2 - 2)/(6 x - 6)

*g(x)=(5x^2+2)/(6x−6) g(3 x)

(45*x^2+2)/(18*x-6)

*Describe :f(x+3)^2

* shift left 3 units

*f(x) = -sqrt(x-4) + 8

*Describe: f(x) = -sqrt(x-4) + 8

*3(x-2)^2+4=14

*Solve :3(x-2)^2+4=14

*p(x)=−4 ln(x) − 4 − p(x)

+ 4*ln(x) + 4

*q(x)=4 + 5 x^2 −q(x)

- 4 - 5 x^2

*h(x)=4 + 7 x + 3 x^2 −h(x)

- 4 - 7 x - 3 x^2

* Transform f(x) = x^2 by shifting right up 3 units and reflect about the x axis

-(x-2)^2-3

*Given f(x) = x^3 shift the graph right 2 units , reflect across the x axis and shift up 3 units

-(x-2)^3+3

*g(x)=(5x^2+2)/(6x−6) g(0)

-1 3

*f(x)=3 + 10x, g(x)=−5x^2 + 5x, and h(x)=6x^2 + 6x + 3, compute and simplify each of the following: g(x) − h(x)

-11x^2-x-3

*f(x)=5 + 7 x f(x− 2)−8

-17 + 7 x

*h(x)=4 + 7 x + 3 x^2 h(x) − 6

-2 + 7 x + 3 x^2

*p(x)=−4 ln(x) − 4 p(e^6)

-28

*q(x)=4 + 5 x^2 q(x)−7

-3 + 5 x^2

*p(x)=−4 ln(x) − 4 p(x + 6)−6

-4 * ln(x + 6) - 10

*f(x)=5 + 7 x −f(x)

-5 - 7 x

*f(x)=3 + 10x, g(x)=−5x^2 + 5x, and h(x)=6x^2 + 6x + 3, compute and simplify each of the following: f(x) ·g(x)

-50x^3+35x^2+15x

*f(x) = ln (x) Shift right 4 units compress 1/4 shift up 1 unit

.25ln(x-4)+1

*H(x)=4x+11 and K(x)=(−3−x)^2, compute and simplify each of the following (K °H)(−1)

100

*h(x)=4 + 7 x + 3 x^2 h(x − 7) + 3

105 - 35 x + 3 x^2

* f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following.. g(f(x))

10x/(10x+1)-1/(10x+1)

*f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following.. g(f(−1))

11/ 9

* f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following. (f °g)(1)

153/ 7

*H(x)=4x+11 and K(x)=(−3−x)^2, compute and simplify each of the following K(H(x))

16x^2+112x+196

* f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following. f(g(−1))

191? 9

*f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following.. f(g(x))

19x/(x-8)-172/(x-8)

*q(x)=4 + 5 x^2 5 q(x) − 3

25*x^2 + 17

*H(x)=4x+11 and K(x)=(−3−x)^2, compute and simplify each of the following H(K(−1)) 27

27

*p(x)=−4 ln(x) − 4 −7 p(−x)

28 * ln(-x) + 28

*f(x)=5 + 7 x f(7 x)−2

3 + 49 x

*H(x)=4x+11 and K(x)=(−3−x)^2, compute and simplify each of the following (H °K)(x)

4x^2+24x+47

*f(x)=5 + 7 x f(−x)

5 - 7 x

*q(x)=4 + 5 x^2 q(x − 4)

5*x^2 - 40 x + 84

*q(x)=4 + 5 x^2 q(x−7)

5*x^2 - 70 x + 249

* f(x) = 5sqrt(x) shift left 3 reflect y axis shift down 7

5sqrt(-x+3) -7

* f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following.. (g °g)(1)

61/ 47

*f(x)=3 + 10x, g(x)=−5x^2 + 5x, and h(x)=6x^2 + 6x + 3, compute and simplify each of the following: f(x) + h(x)

6x^2+16x+6

*Find the inverse of F(x)=−2lnx+8

F−1(x) = exp((x-8)/-2)

*Find the inverse of G(x)=4−5/x

G−1(x) = -5/(x-4)

*Find the inverse of H(x)=9−4ln(x+6)

H−1(x) = exp((x-9)/-4)-6

*Find the inverse of J(x)=−6−(2sqrt(x−6))

J−1(x) = (-6 - x)^2 +6

*Find the inverse of K(x)=8logx+6

K−1(x) = 10^((x-6)/8)

*f(x) =(x-3)^2 +4

Right 3, Up 4

*If c<1 cf(x)

compresses the graph horizontally by a factor of c

*The vertex form of a quadratic equation is

f(x) = a(x-h)^2 +k

*Given f(x) = 1/x write a new equation that has V:A at x = 4and H:A at y = 14

f(x)= 1/ x-4+ 14

*Find the inverse of f(x) = 8x+7

f−1(x) = (x-7)/8

*Write f(x) = x^2 so that i is shifted lefy 6 units and down 9 units

g(x) = (x+6)^2-9

*Find the inverse of g(x)=5x^2 + (−2)

g−1(x) = ((x+2)/(5))^(1/2)

*Find the inverse of h(x)=3x/4

h−1(x) = 4x/3

*f(x)= -(x+4)^2-8

left 4, down 8, reflect x axis, stretch vertically by a factor of 3

*If a < 0 then the quadratic function is opening down

opening down.

*If a >0 then the quadratic function is

opening up

*f(x) = 1/x is a

reciprocal function

*-f(x)

reflects the graph about the x axis

*f(-x)

reflects the graph about the y axis

*f(x) - c means to

shift down c units

*Describe :f(x) = -sqrt(-x+2) - 3

shift left 2 units

* f(x-2)^2

shift right 2 units

*f(x) + c means to

shift up c units

*If c>1 cf(x)

strecthes the graph vertically by a factor of c

* f(x)=10x+9 and g(x)= (x-10)/(x-8) compute and simplify each of the following. f(g(8))

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*g(x)=(5x^2+2)/(6x−6) g(1)

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*Given x^2 where k>0 then x = -sqrt(k) and x=sqrt(k)

x = -sqrt(k) and x=sqrt(k)

*Compose: f(x)= x^2-3x+1 g(x)= x-2 (g-f)(x)=

x^2-3x-1

*Compose: f(x)= x^2-3x+1 g(x)= x-2 (f-g)(x) =

x^2-7x+11