Plz me! function f is shown on the graph below where two points are marked. if function f is horizontally compressed by a factor of 2, plot the two corresponding points that would lie on the transformed function.

the two corresponding points are:

point (-4, 21) and point (4, 4)

Explanation:

We strectch or compress a function horizontally (in the x direction) by multiplying the argument of the function by a constant.
To compress the factor has to be greater than 1.

In this case the factor is 2.

It means that the new function is g(x) = f(2x)

The points given are (-4,5) and (4,-3)

Then the new points are  g(-4) = f(-8) and g(4) = f(8).

You need to find the function f(x) to determine f(-8) and f(8).

The function f(x) is determined using the vertex form.

Vertex form: y = A (x - h)² + k
h and k are the coordinates of the vertex.

From the graph the vertex is (2, -4) ⇒ h = 2, k = - 4

⇒ y = A (x - 2)² - 4

Use other point to find A.

Use the point x = 6, y = 0 ⇒ 0 = A (6 - 2)² - 4 = A(4²) - 4 = 16A - 4

⇒ 16A - 4 = 0 ⇒ 16A = 4 ⇒ A = 4 / 16 = 1 /4
⇒ f(x) = (1/4) (x - 2)² - 4.

Now you can calculate the two points:

g(-4) = f(-8) = (1/4) (- 8 - 2)² - 4 = (1/4) (100) - 4 = 21⇒ point (-4, 21)

g(4) = f(8) = (1/4) (8 - 2)² - 4 = (1/4) 36 - 4 = 4 ⇒ point (4, 4)

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