Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 polnts)
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 Describe Two Types Of Transformations That Can Be Used To Transform Fx To Gx 2 Polnts Part B Solve For K In Each Type Of Transformation 4 Points Part C W class=

Sagot :

varshamittal029

Horizontal and Vertical translations can transform f(x) to g(x).                                                                                                                                                                                                            

Equations to transform f(x) to g(x) are: g(x) = f(x) + k, and g(x) = f(x + k).

In vertical translation k = 18, and horizontal translation k = 6.

Solution

Equations of the two st. lines

Select two points on the line f(x) viz. (1,2), (2,5).

The equation of the line f(x) is

[tex]\frac{y-2}{x-1} = \frac{5-2}{2-1} \Rightarrow \mathbf{y=3x-1}.[/tex]

Select two points on the line g(x) viz. (-5,2), (-4,5).

The equation of the line g(x) is

[tex]\frac{y-2}{x+5} = \frac{5-2}{-4+5} \Rightarrow \mathbf{y=3x+17}.[/tex]

Ways to transform

The two lines, f(x) and g(x), are parallel to each other so their orientation w.r.t. each other is not changed. f(x), thus, can be translated to obtain g(x).

The translation of f(x) can be done in two ways: Vertical translation, and Horizontal translation.

Horizontal translation

f(x) can be translated horizontally to obtain g(x) by the relation of type g(x) = f(x + k).

Using the above relation for the two lines,

3x + 17 = 3(x + k) -1  ⇒  k = 6.

The horizontal translation relation is g(x) = f(x + 6).

Vertical translation

Vertical translation can be done with the relation g(x) = f(x) + k.

Using the above relation for the two lines,

3x + 17 = 3x - 1 + k  ⇒  k = 18.

The vertical translation relation is g(x) = f(x) + 18.

The two transformation relations are: g(x) = f(x + 6), and g(x) = f(x) + 18.

Learn more about the transformation of linear equations here

https://brainly.com/question/17097018

#SPJ10

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.