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ella [17]
3 years ago
7

Write the equation of a piecewise function with a jump discontinuity at x =3. Then, determine which step of the 3-step test for

continuity that the function
fails.

Mathematics
1 answer:
seraphim [82]3 years ago
5 0

Answer:

Here's a possible example:

Step-by-step explanation:

f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}

Each piece is linear, so the pieces are continuous by themselves.

We need consider only the point at which the pieces meet (x = 3).

\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)

The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.

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A population of 130,000 grows 4% per year for 16 years.
alexgriva [62]

Let's consider the scenario after each year:

After the zeroth year, the population is: 120 000(1 + 0.04)⁰

After the first year, the population is: 120 000(1 + 0.04)¹

After the second year, the population is: 120 000(1 + 0.04)²

...

Thus, we can find the general rule:

After the nth year, the population is: 120 000(1 + 0.04)ⁿ

And after the 16th year, the population is 120 000(1 + 0.04)¹⁶ = 224 758 (rounded to nearest whole number)

6 0
3 years ago
Oliver earns $9 per hour. Write and solve an equation to find how many hours he must work to earn $315
natka813 [3]
Y=9x

315=9x

315/9=x

35=x
7 0
2 years ago
Simplify the expression:
krek1111 [17]

Answer:

235a is 1

235b is a^12k+4 i think

3 0
3 years ago
HELP ASAP
serg [7]

The equation of the line which is plotted on the graph and passes from the points (2,5) and (-2,-3) is y=2x-6.

<h3>What is the equation of line?</h3>

The equation of the line is the way of representation of a line in the equation form.

The equitation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.

The formula to find equation of line is,

(y-y₁)={(y₂-y₁)/(x₂-x₁)}(x-x₁)

Here, x and y are the coordinate and subscript (1,2) used for the first and second point.

The points from which the line passes through are (2,5) and (-2,-3). Put the values,

(y-y₁)={(y₂-y₁)/(x₂-x₁)}(x-x₁)

(y-(-2))={(-3-5)/(-2-2)}(x-2)

y+2={-8/-4}(x-2)

y+2=2(x-2)

y+2=2x-4

y=2x-4-2

y=2x-6

Thus, the equation of the line which is plotted on the graph and passes from the points (2,5) and (-2,-3) is y=2x-6.

Learn more about the equation of line here;

brainly.com/question/13763238

#SPJ1

3 0
2 years ago
two-fifth of the fish in Gary's fish tank are guppies. One-fourth of the guppies are red. What fraction of the fish in Gary's ta
Gennadij [26K]

Answer:

1/10

Step-by-step explanation:

To find the number of red guppies, multiply the fractions.

Gary has 2/5 of his fish collection as guppies. Of the guppies, 1.4 are red.

So 2/5 * 1/4 = 2/20 = 1/10.

7 0
3 years ago
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