If answered correctly, I will give brainliest and 30 points. i also need this asap. The linear functions f(x) and g(x) are represented

Question

If answered correctly, I will give brainliest and 30 points. i also need this asap.
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.

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)

in progress 0
Delwyn 4 years 2021-08-28T00:53:11+00:00 2 Answers 278 views 0

Answers ( )

  1. MichaelMet
    1
    2021-08-28T00:54:47+00:00
    Reply

    hmm can’t see the questions

  2. giabao
    0
    2021-08-28T00:55:05+00:00
    Reply

    Answer:

    First, let’s find the equations for our lines:

    A linear relationship can be written as:

    y = a*x + b

    where a is the slope and b is the y-axis intercept.

    For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

    a = (y2 – y1)/(x2 – x1).

    f(x) passes through (5,0) and (10, 10), then the slope is:

    a = (10 – 0)/(10 – 5) = 10/5 = 2.

    then we have:

    y = 2*x + b

    And when x = 5, we have y = 0.

    0 = 2*5 + b

    0 = 10 + b

    b = -10

    Then the equation for f(x) is:

    y = f(x) = 2*x – 10.

    Now for g(x) we have the points:

    (3, 0) and (2, 10)

    a = (10 – 0)/(2 – 3) = -10

    y = -10*x + b

    0 = -10*3 + b

    b = 30.

    y = g(x) = -10*x + 30.

    A) Ok, the transformations:

    Transformation 1 or T1.

    f(x) = 2*x – 10

    g(x) = -10*x + 30.

    Then, we start with f(x):

    First, we can move f(x) up 4 units and get:

    f'(x) = 2*X – 6

    Now we can dilate f(x) with a scale factor of -5 from the origin, now we get:

    f”(x) = -5*f'(x) = -10*x + 30.

    And this is g(x).

    Transformation 2 or T2.

    Move f(x) up 10 units, so now we have:

    f'(x) = 2*x

    Do a reflection over the x-axis, so the sign of y changes, and now we get:

    f”(x) = -2*x

    Do a dilation of scale factor 5

    f”'(x) = 5*-2*x = -10*x

    Now do a vertical translation of 30 units up.

    f””(x) = -10*x + 30 = g(x).

    These are two transformations that start with f(x) and end with g(x).

    B) Ok, as i was writting the transformations i already solved them, so this part is already done.

    C) the equation for the transformations are:

    T1) g(x) = -5*(f(x) + 4)

    T2) g(x) =  -(f(x) + 10)*5 + 30

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