Question

please helpthe linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x)

Answer 1

Part A

The transformation of f(x) to g(x) is a translation

two types

First

translation in x direction

the rule is

(x,y) ------> (x+k1,y)

second

translation in y direction

(x,y) -----> (x,y+k2)

Part B

solve for k

First

(x,y) ------> (x+k1,y)

the x-intercept of f(x) is 5

the x-intercept of g(x) is -3

so

(x,y) ------> (x-8,y)

the translation is 8 units to the left

k1=-8

Second

(x,y) -----> (x,y+k2)

the y-intercept of f(x) is -10

the y-intercept of g(x) is 6

so

(x,y) -----> (x,y+16)

the translation is 16 units up

k2=16

Part C

write an equation for each type of transformation

First

(x,y) ------> (x-8,y)

so

g(x)=f(x+8)

second

(x,y) -----> (x,y+16)

so

g(x)=f(x)+16