1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Radda [10]
3 years ago
15

Confused on how to do these Piecewise-Defined evaluations..

Mathematics
2 answers:
expeople1 [14]3 years ago
8 0

check the picture below.


notice the dashed lines, those are the "continuations" lines for the subfunction of the piecewise, however, the subfunctions have a range each, so that part is not part of the piece-wise function.

anyway, notice, the solid dots on the ends mean, that endpoint number is included, and the "holes" in the ends, mean that endpoint is not included, or not part of the range, something like 2 < x, simply means, "x" is greater than 2, but not 2 itself, so 2 is not a value for "x", just greater numbers.

so, you can see there what f(1), f(3) and f(2) are, hmmm what happened to f(-5)?  well, is out of range, is not part of the piece-wise, so N/A (not available).

Gekata [30.6K]3 years ago
6 0

See the attached image for the graph. The piecewise function is simply a collection of functions glued together to form a sort of "frankenstein function" of sorts. Here's how it works. If x is between 0 and 1 (including 0 but excluding 1), then f(x) = -2 for all x values mentioned. This is exactly what the first row of the piecewise function says. Then the second line says "if x is between 1 and 2, including both endpoints, then f(x) = 3-x". Finally the last line says f(x) = 1 as long as x is larger than 1 but smaller than 4. The value x = 4 is allowed for this piece but x = 1 is not allowed.

--------------------------------------------------

Now onto function evaluation. We want to evaluate f(1) so we need to find f(x) when x = 1. If x = 1, then we'll use the second piece because the first piece excludes x = 1. So

f(x) = 3-x

f(1) = 3-1

f(1) = 2

is the first answer for the function evaluation section.

The value of f(3) is equal to 1 since we resort to using the third piece of the piecewise function (x = 3 is in the range from x = 2 to x = 4)

The value of f(-5) is undefined simply because we're out of the range defined by the piecewise function. The smallest x can get is x = 0.

Finally, f(2) is equal to 1 since...

f(x) = 3-x

f(2) = 3-2

f(2) = 1

again we use the second piece of the piecewise function because x = 2 is in the range 1 <= x <= 2

--------------------------------------------------

In summary:

f(1) = 2

f(3) = 1

f(-5) = undefined

f(2) = 1

Once again have a look at the graph to see how the points match up. I've color-coded the graph so that each piece is a different color. The first piece is in red, the second in blue, the third in green. Note the open hole at point B to indicate "don't include this point as part of the graph".

You might be interested in
Question 9
yan [13]
Answer: —> (d).........
5 0
3 years ago
The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in p
tigry1 [53]

Answer:

f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}

Step-by-step explanation:

Recall that a <em>probability mass function</em> defined on a discrete random variable X is just a function that gives the probability that the random variable equals a certain value k

f_X(k)=P(X=k)

In this case we have the event  

“The computer will ask for a roll to the left when a roll to the right is appropriate” with a probability of 0.003.

Then we have 2 possible events, either the computer is right or not.

Since we have 4 computers in parallel, the situation could be modeled with a binomial distribution and the probability mass function

f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}

This gives the probability that k computers are wrong at the same time.

6 0
3 years ago
A car travels 0.75 miles every minute
Ilya [14]

Answer:

I think you may have forgot to put in the rest of the question mate

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Rewrite the equation of the parabola in vertex form.
aleksandrvk [35]
The answer would be y=(x+4)^2-37
5 0
3 years ago
(2+x)dy/dx=3y need help
den301095 [7]
(2+x) \frac{dy}{dx} =3y
\frac{1}{3y} dy= \frac{1}{2+x} dx
\int { \frac{1}{3y} } \, dy = \int { \frac{1}{2+x} } \, dx
\frac{1}{3}\ln(3y) = \ln(2+x) + C
(raise both to the power e): e^{ \frac{1}{3}\ln(3y)}=e^{\ln(k(2+x))}
(3y)^ \frac{1}{3} =k(2+x)
3y=k(2+x)^3
y= k(2+x)^3
5 0
3 years ago
Other questions:
  • Order the periods of time from least to greatest.
    11·1 answer
  • Use the following figure to answer the question. 5 and 7 are ____ angles.
    6·2 answers
  • I will give brainlist for correct answer.
    5·2 answers
  • Given the function f(x) = 7x² – 3x + 6. Calculate the following values:
    15·1 answer
  • Examine the diagram. Parallel lines a and b are crossed by transversal t to create 8 angles. Clockwise from top left, the angles
    13·2 answers
  • at a certain fast-food restaurant, the volume of a large soda is 35% greater than the volume of a small soda. if the volume of t
    14·1 answer
  • Please Help!!!: <br> ( in a hurry!)<br><br> Will name the Brainliest!
    5·1 answer
  • A cone has a height of 16 inches and a radius of 12 inches. What is its volume?
    9·2 answers
  • Brianna is about to list her house as For Sale By Owner. She would like to receive a minimum of $213,000 on the sale, but she al
    11·1 answer
  • Which function represents a parabola that is translated 2 units to the left and 6 units down from the parent function, f(x)=x^2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!