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
meriva
2 years ago
5

Express the function graphed on the axes below as a piecewise function.

Mathematics
1 answer:
adoni [48]2 years ago
3 0

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

You might be interested in
10(8+3h) need help asap
LuckyWell [14K]

Answer:

80 + 30h

Step-by-step explanation:

10(8+3h)

Distribute

10*8 + 10*3h

80 + 30h

3 0
3 years ago
Read 2 more answers
3. What is the slope of the table shown? Cars Washed Number Money ($) 5 40 10 80 15 120 20 160​
IceJOKER [234]
The slope is 8.
(5,40) (10,80)
80-40=40
10-5=5
40/5=8
3 0
2 years ago
What is the value of y when x = 43<br> A. 87<br> B. 85<br> C. 49<br> D. 45
BartSMP [9]

Answer:

A x

=

3

,

−

1x

=

3

,

−

1

Step-by-step explanation:

x

=

3

,

−

1

3 0
2 years ago
Please help, I will mark Brainliest.
Goshia [24]
It’s rational because the square root of 0.49 is 0.7
3 0
3 years ago
Which one doesn't belong?
Montano1993 [528]

Answer:

A 17

B 11.5

Step-by-step explanation:

5+2=7+2=9+2=11+2=13+2=15+2=17

and please check ur question C and D

7 0
3 years ago
Other questions:
  • Ircle the letter of the correct digit. in the measurement 43.52 cm, which digit is the most uncertain?
    11·1 answer
  • Determine if sequence is arithmetic or geometric. Then find the next term in the sequence. Select all that apply. 2, 10, 50, 250
    7·2 answers
  • Simplify the equation 28st/-4t
    12·1 answer
  • Evaluate.
    13·1 answer
  • 3/4•3/4???? I can’t do it in my head and I don’t know how to make a decimal into a fraction
    13·2 answers
  • Find the unknown measure ASAP please....
    8·2 answers
  • George borrowed $25,000 for a new car. If George pays simple interest at a rate of
    13·2 answers
  • T
    12·2 answers
  • What is the value of h
    11·1 answer
  • 6 Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995),
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!