The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Part A) shift left 6 units or shift up 18 units

Part B) k=-6 and k=18

Part C) g(x)=f(x+6)  or g(x)=f(x)+18

Step-by-step explanation:

Find the equation of f(x)

we have the points(0,-1) and (2,5)

The slope m is

The equation in slope intercept form is

we have

substitute

Find the equation of g(x)

we have the points (-1,14) and (0,17)

The slope m is

The equation in slope intercept form is

we have

substitute

Part A and Part B: Describe two types of transformations that can be used to transform f(x) to g(x). Solve for k in each type of transformation

First type of transformation

we have

Find the x-intercepts of f(x) and g(x) (values of x when the value of the function is equal to zero)

For f(x)=0

For g(x)=0

f(x) -----> g(x)

The translation of the x-intercept is

(1/3,0) --------> (-17/3,0)

so

The rule of the translation is

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

(1/3,0) -----> (1/3+k,0)

so

(1/3+k,0)=(-17/3,0)

Solve for k

Multiply by 3 both sides

therefore

The rule of the translation is

(x,y) -----> (x-6,y)

That means -----> The translation is 6 units at left

Second type of transformation

we have

The y-intercepts (values of the function when the value of x is equal to zero)

f(x) -----> (0,-1)

g(x) ----> (0,17)

The translation of the y-intercept is

f(x) ---->g(x)

(0,-1) --------> (0,17)

so

The rule of the translation is

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

(0,-1) -----> (0,-1+k)

so

(0,-1+k)=(0,17)

Solve for k

therefore

The rule of the translation is

(x,y) -----> (x,y+18)

That means -----> The translation is 18 units up

Part C) Write an equation for each type of transformation that can be used to transform f(x) to g(x).

First transformation

The rule of the translation is

(x,y) -----> (x-6,y)

f(x) -----> g(x)

g(x)=f(x+6)

so

therefore

----> is correct

Second transformation

The rule of the translation is

(x,y) -----> (x,y+18)

f(x) -----> g(x)

so

----> is correct

step-by-step explanation:

; fx

answer: ay  

fonsi  

dy  

oh

oh no, oh no

oh yeah

diridiri, dirididi daddy  

go

sí, sabes que ya llevo un rato mirándote  

tengo que bailar contigo hoy (dy)  

vi que tu mirada ya estaba llamándome  

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal  

me voy acercando y voy armando el plan  

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal  

todos mis sentidos van pidiendo más  

esto hay que tomarlo sin ningún apuro

despacito  

quiero respirar tu cuello despacito  

deja que te diga cosas al oído  

para que te acuerdes si no estás conmigo

despacito  

quiero desnudarte a besos despacito  

firmo en las paredes de tu laberinto  

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)