Foxgirl182
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We are learning about Parent functions in class, can someone explain how to do this? I’m having trouble. 1.) g(x)=x^2-1. Parent:? Transformation: ? 2.) f(x)= 2|x-1|. Parent: ? Transformation: ? 3.) h(x)=-1/x. Parent: ? Transformation: ? 4.) g(x)=-2(x+1)^2+3. Parent: ? Transformation: ? 5.) g(x)=-3x-2. Parent: ? Transformation: ? 6.) f(x)=(x+1)^2-2. Parent: ? Transformation: ? 7.) h(x)=(x+2)^3. Parent: ? Transformation: ? 8.) h(x)= -|x-2|. Parent: ? Transformation: ? 9.) h(x)=6(x+9)^2. Parent: ? Transformation: ?

Sagot :

sqdancefan

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Answer:

  1. parent: g(x) = x^2; transformation: translate down 1
  2. parent: f(x) = |x|; transformation: vertical expansion by factor of 2, translation right 1.
  3. parent: 1/x; transformation: reflection across the x-axis

Step-by-step explanation:

The parent function is what you have left when every multiplying factor is replaced by 1, and every added numerical value is replaced by zero.

The typical transformations we're concerned with are ...

  • vertical expansion by a factor of c: y = c·f(x)
  • horizontal expansion by a factor of c: y = f(x/c)
  • translation (right, up) by (h, k): y = f(x -h) +k

If the value of expansion factor (c) is negative, there is a reflection across the relevant axis. Vertical reflection is across the x-axis; horizontal reflection is across the y-axis.

When the "expansion" factor is less than 1, the result is a compression. Authors vary in describing compression. Some would say compression by a factor of 2 makes the image smaller; others would describe the same transformation as compression by a factor of 1/2. YMMV

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9 questions is beyond the scope of a single Brainly answer, so we'll give you some examples.

  1. g(x) = x^2 -1

replacing -1 with 0, we find the parent function to be g(x) = x^2.

The added value of -1 means the transformation is a translation down 1 unit.

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  2. f(x) = 2|x -1|

replacing the multiplier 2 with 1, and the added -1 with 0 gives the parent function f(x) = |x|.

The multiplier means the function is expanded vertically by a factor of 2. The replacement of x with (x-1) means the function is translated right 1 unit.

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  3. h(x) = -1/x

replacing the multiplier -1 with 1 gives the parent function h(x) = 1/x.

The negative sign on the vertical expansion factor means the transformation is a reflection across the x-axis.

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Additional comment

You will see these transformations a lot, and in various combinations. It is a good idea to practice recognizing them. Pay particular attention to the signs related to translation.

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