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Virty [35]
3 years ago
12

The range of the function y=secx-2 is all reals except -1 1 -3 -2

Mathematics
1 answer:
Umnica [9.8K]3 years ago
6 0

Answer:

For a function y = f(x), the range is the set of all the possible values of y.

In the question you wrote:

y = secx - 2

This can be interpreted as:

y = sec(x - 2)

or

y = sec(x) - 2

So let's see each case (these are kinda the same)

If the function is:

y = sec(x - 2)

Firs remember that:

sec(x) = 1/cos(x)

then we can rewrite:

y = 1/cos(x - 2)

notice that the function cos(x) has the range -1 ≤ y ≤ 1

Then for the two extremes we have:

y = 1/1 = 1

y = 1/-1 = -1

Notice that for:

y = 1/cos(x - 2)

y can never be in the range  -1 < x < 1

As the denominator cant be larger, in absolute value, than 1.

Then we can conclude that the range is all reals except the interval:

-1 < y < 1

If instead the function was:

y = sec(x) - 2

y = 1/cos(x) - 2

Then with the same reasoning, the range will be the set of all real values except:

-1 - 2 < y < 1 - 2

-3 < y < -1

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Answer:

\frac{1}{6} p - \frac{4}{5}

Step-by-step explanation:

collect like terms

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= - \frac{2(2)}{2(3)} p + \frac{5}{6} p + \frac{1}{5} - \frac{5}{5}

= - \frac{4}{6} p + \frac{5}{6} p - \frac{4}{5}

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1 year ago
If J = 12 then J/3 + 3 What is J
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6 0
3 years ago
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There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced
Harlamova29_29 [7]

Answer:

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Step-by-step explanation:

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Exponential functions such as this are of the form

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3 years ago
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Hello,

Shall we begin?

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Answers: 30
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