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3. Are these the hills teen 1 was trying to design? Remember, teen 1 wanted one layer

of three hills, another set of three hills using the same base equation, and one long,

low hill. Find any mistakes that teen 1 made in his design and in the reasoning he

presented when explaining the transformations of the equations. (3 points)

Respuesta :

MrRoyal

Function transformation involves changing the form of a function

  • The first mistake in teen 1's design is the x-intercepts
  • The second mistake in teen 1's design is the transformed function

The function that represents the three hills is given as:

[tex]f(x) = (x - 1)(x -3)(x -4)[/tex]

The above function represents the base equation.

When the function is then transformed, we have:

[tex]g(x) =- (x - 1)(x -3)(x -4) + 3[/tex]

The first mistake in teen 1's design is that, the function f(x) has 3 x-intercepts

For the function to have three peaks, then the function must have three different vertices

A function with three x intercepts will have three zeros.

However, these three zeros does not mean the function has three peaks i.e. three vertices

Also, the transformed function g(x) is simply a reflection of f(x) across the x-axis, and a vertical shift up by 3 units.

This also does not mean that the function has three peaks

Read more about function transformation at:

https://brainly.com/question/11861033

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