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))
undefined
*g(x)=(5x^2+2)/(6x−6) g(1)
undefined
*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