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Evgen [1.6K]
3 years ago
6

The graph of an absolute value function opens down and has a vertex of (-3,0).

Mathematics
2 answers:
QveST [7]3 years ago
8 0
<h2>Answer:</h2>

The domain of the function is:

                All real numbers i.e. (-∞,∞)

The range of the function is:

                     (-∞,0]

<h2>Step-by-step explanation:</h2>

It is given that:

The graph of an absolute value function opens down and has a vertex of (-3,0).

This means that the graph of the function increases continuously in the interval (-∞,-3] and takes maximum value 0 when x= -3 and then decreases continuously in the interval (-3,∞).

<u>Domain of a function--</u>

It is the set of all the x-values for which a function is defined i.e. it is the set of all the values of the independent variable for which the function is defined.

<u>Range of a function--</u>

It is the set of all the values attained by a function.

  • We know that a absolute value function is defined all over the real line i.e. the domain of the function is the set of all the real values i.e. (-∞,∞).
  • Also, the function takes all the value between -∞ and 0 and 0 is included.

                Hence, the range of the function is: (-∞,0].

dsp733 years ago
3 0
I wrote the domain and range in interval notation, not sure if that’s how you’re asked to do it. This is how I was taught to state the domain/range of a graph.

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The statue of Liberty stands on a 150 ft. pedestal. From a point 250 ft. from the base of the
bekas [8.4K]

Answer:

148ft

Step-by-step explanation:

To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.

Assuming the height from the pedestal to the top of the torch is y

The height of the statue is x

But we know the height of the pedestal = 150ft

The distance from the observer to the base of the pedestal = 250ft

And the angle of elevation = 50°

See attached document for better illustration.

Tanθ = opposite / adjacent

θ = 50°

Adjacent = 250

Opposite = y

Tan50 = t / 250

y = 50 × tan50

y = 50 × tan50

y = 50 × 1.1917

y = 297.925ft

The height of the statue from the base of the pedestal to the top of the torch is 297.925ft

The height of the statue = x

x = (height of the statue + height of the pedestal) - height of the pedestal

x = y - 150

x = 297.925 - 150

x = 147.925ft

Approximately 148ft

The height of the statue is 148ft

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