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marin [14]
2 years ago
5

Given the parent function f(x)=|x|, write the equation of the function g(x) whose graph is pictured

Mathematics
1 answer:
kenny6666 [7]2 years ago
5 0

By analyzing the graph of the transformed function, we can see that:

g(x) = 2*|x - 2| - 4

<h3>How to get the function g(x)?</h3>

In the image we have two graphs, the yellow one is the graph of g(x).

First, analyzing the vertex we can see the translation used, you need to remember:

<u>Horizontal translation:</u>

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

  • If N is positive, the shift is to the left.
  • If N is negative, the shift is to the right.

<u>Vertical translation:</u>

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

  • If N is positive, the shift is upwards.
  • If N is negative, the shift is downwards.

We can see that the new vertex is at (2, -4), so the translation is 2 units to the right and 4 units down, then we have:

g(x) = |x - 2| - 4

Now, you also can see that the yellow function is narrower, such that for each increase in the x-unit, we have an increase of 2 in the y-axis, then we need to multiply by 2 the absolute value part:

g(x) = 2*|x - 2| - 4

This is the transformed function.

If you want to learn more about transformations, you can read:

brainly.com/question/4289712

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What are the measures of the angles in triangle ABC?
VMariaS [17]

Complete question :

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

What are the measures of the angles in triangle ABC?

a) m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°

b) m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°

c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

d) m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°

Answer:

c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

Step-by-step explanation:

Given:

Length AC = 7 inches

Length BC = 24 inches

Length AB = 25 inches

Since it is a right angle triangle,

m∠C = 90°

To find the measures of the angle in ∠A and ∠B, we have :

For ∠A:

SinA = \frac{BC}{AB}

SinA = \frac{24}{25}

SinA = 0.96

A = Sin^-^1 = 0.96

∠A = 73.7°

For ∠B:

SinB = \frac{AC}{AB}

SinB = \frac{7}{25}

SinB = 0.28

B = Sin^-^1 = 0.96

∠B = 16.26 ≈ 16.3°

Therefore,

m∠A = 73.7°

m∠B = 16.3°

m∠C = 90°

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