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3 years ago

The exponential function f(x) has a horizontal asymptote at y=3 what is the end behaviour of f(x)?

Mathematics

1 answer:

tatuchka [14]3 years ago

8 0

Answer: C) as x → -∞, y → 3

as x→ ∞ , y → ∞

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

see graph

Notice that as x approaches negative infinity (goes to the left), the y value approaches the asymptote of y = 3.

And as x approaches positive infinity (goes to the right), the y-value increases without bound so goes to infinity.

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What relations are functions

Inessa05 [86]

The requirement is that every element in the domain must be connected to one - and one only - element in the codomain.

A classic visualization consists of two sets, filled with dots. Each dot in the domain must be the start of an arrow, pointing to a dot in the codomain.

So, the two things can't can't happen is that you don't have any arrow starting from a point in the domain, i.e. the function is not defined for that element, or that multiple arrows start from the same points.

But as long as an arrow start from each element in the domain, you have a function. It may happen that two different arrow point to the same element in the codomain - that's ok, the relation is still a function, but it's not injective; or it can happen that some points in the codomain aren't pointed by any arrow - you still have a function, except it's not surjective.

6 0

3 years ago

A culture started with 5,000 bacteria. After 2 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after

lesya [120]

This can be expressed as exponential growth of the form:

f=ir^t, f=final amount, i=initial amount, r=common ratio (rate), t=time

In this case we are given the point (2, 6500) and i=5000 so we can solve for the rate...

6500=5000r^2 divide both sides by 5000

1.3=r^2 take the square root of both sides and note that we know r>0

r=1.3^(1/2) so our equation becomes:

f=5000(1.3)^(1/2)^t and knowing that (a^b)^c=a^(b*c) we can say:

f=5000(1.3)^(t/2) so for t=18

f=5000(1.3)^9

f≈53022 (to nearest whole bacteria)

7 0

3 years ago

Find the x-values that are solutions of the equation 5cot^2x-15=0

julia-pushkina [17]

First solve for the trig function 'cot'
$cot^2 x = \frac{15}{5} = 3$

Next take the sqrt of both sides (include plus/minus)
$cot x = \pm \sqrt{3}$

Now take reciprocal of both sides, this will change trig function to 'tan'
(cot = 1/tan)

$tan x = \pm \frac{1}{\sqrt{3}} = \pm \frac{\sqrt{3}}{3}$

Finally use the unit circle or inverse tan on your calculator to find x.
There will be 4 solutions, one for each quadrant.

$x = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}$

3 0

3 years ago

The elevation if New Orleans, Lousiana is 8 feet below sea level. The elevation of Lake Champion, Vermont, is 95 feet above sea

Maurinko [17]

Answer:

87 feet

Step-by-step explanation:

8 feet below sea level would be -8

95 feet above sea level would be +95

so it would be -8+95

-8+95=87

3 0

3 years ago

Solve for g : 3+2g=5g-9

KiRa [710]

3+2g=5g-9
5g-2g=3+9
3g=12
3g/3=12/3
g=4

5 0

3 years ago