Mathematics, 09.07.2019 23:00 kelchalyssa

Describe the continuity of the graphed function. select all that apply.

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Answer from: applesass

we know that

Any function f(x) is continuous at x=a only if

$\lim_{x \to a-} f(x) = \lim_{x \to a+} f(x)=f(a)$

We can see that this curve is smooth everywhere except at x=-1

so, we will check continuity at x=-1

Left limit is:

$\lim_{x \to -1-} f(x) = 0$

Right limit is:

$\lim_{x \to -1+} f(x) = 1$

Functional value:

f(-1)= 1

we can see that left limit is not equal to right limit

so, limit does not exist

so, this function is discontinuous at x=-1

Since, limit does not exists

so, there will be jump discontinuity at x=-1

so, option-C........Answer

Answer from: brandiwingard

The answer is A and C

Step-by-step explanation:

You could tell by seeing the plot of a function that it has a discontinuity if you can't trace ir without lifting your pen from the sheet, as you can see, you have to lift your pen in x = -1.

you can make it by math too.

if you remember the concept a function f(x) is continuous at x = a if

$\lim_{x \to \ a^{+}} f(x) = \lim_{x \to \a^{-} } f(x) = f(a)\\$

as you can see by looking at x = -1

$\lim_{x \to \-1^{-}} f(x) = 0\\ \lim_{x \to \-1^{+}} f(x) = 1\\$

as you can see the lateral limits are different so int means that the function is not continuous.

But there's another right answer

the first option A says that the function is continuous at x = -4

let's proof it again

$\lim_{x \to \-4^{-}} f(x) = 3\\ \lim_{x \to \-4^{+}} f(x) = 3$

in this case both limits are equal, but this is not reason enough, we have to proof that the function at x = -4 exists. Does it?, let's check

F(-4) = 3 by looking at the graph so the lateral limits are equal and the function in this value exist so the function is continuous at x = -4

Correct answer is A and C

Answer from: Quest

step-by-step explanation:

Answer from: Quest

$w\geq 14$

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

$2l+2w\geq 40$

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

$2\times 6+2w\geq 40$

now, we can solve for w

$12+2w\geq 40$

subtract both sides by 12

$12+2w-12\geq 40-12$

$2w\geq 28$

divide both sides by 2

and we get

$w\geq 14$

so,

the smallest possible measurement of the width is 14 feet

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Describe the continuity of the graphed function. select all that apply....

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