4. Transformations

Question 1

6 transformations

Answer 1

y = f(x) +- a

y = -f (x)

y = kf(x)

y = f (x +- a)

y = f (-x)

y = f (kx)

Question 2

y = f(x) +-a

Answer 2

y = f (x) + 1 moves graph up vertically
y = f(x) - 1 moves graph down vertically

Change in vertical -> change in y coordinate

Question 3

y = f(x+-a)

Answer 3

y = f (x+a) moves graph horizontally in the negative direction
y = f (x-a) moves graph horizontally in the positive direction

change in horizontal -> change in x coordinate

Question 4

y = -f (x)

Answer 4

y = -f(x) graph is mirrored in x axis

mirrored in x axis -> sign on y coordinate flips

Question 5

y = f (-x)

Answer 5

y = (-x) mirrors graph in y axis

mirrors in y axis = sign on x coordinate flips

Question 6

y = kf (x)

Answer 6

change in multiplier -> multiply y coordinates by multiplier

stretches or compresses graph vertically

Question 7

y = f (kx)

Answer 7

multiplier on x -> divide x coordinate by multiplier

will stretch or compress graph horizontally

if k > 1, graph compresses
if 0 < k < 1 graph stretches

Question 8

Composite functions

Answer 8

Apply more two or more transformations to a function

Question 9

Apply more two or more transformations to a function

Answer 9

composite function

Question 10

Order of operations for composite transformations

Answer 10

Apply in the order of BODMAS

Question 11

what are the coordinates of y = 3 - f (x) for these coords:

(-7, 0)
(-2, 7)
(0, 6)
(2, 5)

Answer 11

(-7, 3)
(-2, -4)
(0, -3)
(2, -2)

Question 12

Find the value of a in y = a^x, a > 0. The graph has the points (0, 1) and (2, 9)

Answer 12

a = 3

Question 13

finding value of a in exponential from known points method

Answer 13

use known points in y = ax

solve for a

Question 14

Find a and b for the exponential graph in the form y = a^x + b with the points (3, 9) and (0, 2)

Answer 14

a = 2

b = 1

Question 15

The graph of y = loga (x + b) has the points (-3, 0) and (4, 1). Find the values of a and k

Answer 15

a = 8

k = 4