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 2 units or shift up 10 units

Part B) k=-2 and k=10

Part C) g(x)=f(x+2)  or g(x)=f(x)+10

Step-by-step explanation:

Find the equation of f(x)

we have the points(0,-2) and (1,3)

The slope m is

The equation in slope intercept form is

we have

substitute

Find the equation of g(x)

we have the points(0,8) and (-1,3)

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

(0.4,0) > (-1.6,0)

so

The rule of the translation is

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

(0.4,0) > (0.4+k,0)

so

(0.4+k,0)=(-1.6,0)

Solve for k

0.4+k=-1.6 > k=-1.6-0.4=-2.0

therefore

The rule of the translation is

(x,y) > (x-2,y)

That means > The translation is 2 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,-2)

g(x) > (0,8)

The translation of the y-intercept is

f(x) >g(x)

(0,-2) > (0,8)

so

The rule of the translation is

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

(0,-2) > (0,-2+k)

so

(0,-2+k)=(0,8)

Solve for k

-2+k=8 > k=8+2=10

therefore

The rule of the translation is

(x,y) > (x,y+10)

That means > The translation is 10 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-2,y)

f(x) > g(x)

so

so

therefore

> is ok

Second transformation

The rule of the translation is

(x,y) > (x,y+10)

f(x) > g(x)

so

so

therefore

> is ok