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Marina86 [1]
3 years ago
13

ACK HELP ITS DUE IN TWENTY MINUTES

Mathematics
1 answer:
NeX [460]3 years ago
5 0

Answer:Number 2

Step-by-step explanation:

For Number 2 Use This Table And Graph

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Answer:

<u>1. Type of function</u>: absolute value function

<u>2. The three transformations from the parent function f(x) = |x| are</u>:

  • Translation 3 units to the left
  • Vertical stretch with a scale factor of 2
  • Translation 5 units downward

Explanation:

<u>1. Type of function</u>

The parent function |x| is the absolute value function. It returns the positive value of the argument (x).

Thus the function f(x) = 2|x + 3| - 5 is also an absolute value function.

It returns the positive value of x + 3, then multiplyes it by 2, and finally subtract 5.

This is a piecewise function.

For the values of x ≥ - 3, the output is 2(x +3) - 5 = 2x + 6 - 5 = 2x + 1.

For the values of x < - 3, the output is 2 (-x - 3) - 5 = -2x - 6 - 5 = -2x - 11.

The vertex of this function is at x = - 3: 2 (- 3 + 3) - 5 = 2(0) - 5 = 0 - 5 = 5.

Thus the vertex is (-3, 5).

<u>2. Transformations from the parent function f(x) = |x|</u>.

When you know the parent function and the daughter function you can know the transformations done of the former to get the later by some simple rules.

a)<u> Translation in the horizontal direction</u>.

When you add a positive value to the argument the function is translated to the left.

Thus, when you add 3 to x, |x| becomes |x + 3| and it is a translation 3 units to the left.

b) <u>Vertical stretch</u>

When you multiply the argument by a constant, the function stretches vertically.

Thus, when you multiply |x + 3| by 2, to get 2|x + 3|, the function is vertically stretched by a scale factor of 2.

c) <u>Vertical translation</u>

When you subtract a constant value from the function, you translate it downward.

Thus, when you subtract 5 from 2|x + 3| - 5, you translate the function 5 units downward.

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