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
alex41 [277]
3 years ago
9

Consider the piecewise-defined function given by the graph. What are these values?

Mathematics
2 answers:
maksim [4K]3 years ago
6 0

Answers:

f(-3) = -1

f(-1) = 2

f(3) = 5

======================================

Explanations:

Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.

Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1

Through similar steps, you should find that f(-1) = 2 and f(3) = 5

Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.

Luda [366]3 years ago
3 0

A) f (–3) = -1

B) f (–1) = 2

C) f (3) = 5

<h3>Further explanation </h3>

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

<h3>y-y1 = m (x-x1) </h3>

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

or we can use:

\rm \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}

Piecewise Functions: functions that have different equations based on the input (x) value

We look for 3 pieces of function from the graph

1. graph 1 is a straight line that passes through 2 points : (-4.0) and (-1, -3) so that the straight line equation:

\rm \dfrac{y-0}{-3-0}=\dfrac{x+4}{-1+4}\\\\\dfrac{y}{-3}=\dfrac{x+4}{3}\\\\3y=-3(x+4)\\\\3y=-3x-12\\\\y=-x-4\Rightarrow \:for\:x

2. graph 2 is a straight line with the equation: \

\rm y=2\Rightarrow \:for\:-1\leq x

3. graph 1 is a straight line that passes through 2 points,  (3.5) and (5.1) so that the straight line equation  :

\rm \dfrac{y-5}{1-5}=\dfrac{x-3}{5-3}\\\\\dfrac{y-5}{-4}=\dfrac{x-3}{2}\\\\2(y-5)=-4(x-3)\\\\2y-10=-4x+12\\\\2y=-4x+22\\\\y=-2x+11\:\Rightarrow for\:x\geq   3

A function made up of 3 pieces:

a solid dot means "including",

an open dot means "not including"

\rm y=-x-4\:for\:x

\rm y=2\:for\:-1\leq x

\rm y=-2x+11\:for\:x\geq 3

A) f (–3) =

Because -3 <-1, the function used is y = -x-4, so

f (-3) = - (- 3) -4

f (-3) = 3-4

f (-3) = -1

B) f (–1) =

Because x = -1, the function used y = 2, so

f (-1) = 2

C) f (3) =

Because x = 3, the function used is = -2x + 11, so

f (3) = -2 (3) +11

f (3) = -6 + 11

f (3) = 5

<h3>Learn more </h3>

Piecewise Functions

brainly.com/question/1242635

the inverse of the function

brainly.com/question/628130

domain of the function

brainly.com/question/4135536

You might be interested in
Mini made a recipe that yields 4 1/2 cups if each serving is 1/2 cup which expression will help many determine the number of ser
Black_prince [1.1K]

You have to divide the total about of cups by the serving size:

4 1/2 divided by 1/2 and you get the answer.

4 1/2 converted into an improper fraction is 9/2.

9/2 divided by 1/2 = 9

8 0
3 years ago
Read 2 more answers
(x² - 6x + 3) (8x² + 7x + 9) = ​
ololo11 [35]

Answer:

8x^4 - 41x^3 - 9x^2 - 33x + 27

Step-by-step explanation:

The screenshot given below will hopefully help you :)

8 0
3 years ago
Could someone please help ;(
Iteru [2.4K]

Answer:

a. 25/33

b. 36

c. 1/15

d. 35/12

e. 19/12

7 0
3 years ago
Read 2 more answers
10.6 written as a decimal and a fraction or a mixed number in simplest form
lakkis [162]
10.6 \times \frac{10}{10} = \frac{106}{100} = \frac{53 \times 2}{50\times 2} \\\\ = \frac{53}{50} = \boxed{\bf{1 \frac{3}{50}}}

and 10.6 is already written as a decimal.
6 0
3 years ago
Find the value of x in the proportion 4/7 = x 56 pls help!!
serg [7]

Answer:

98

Step-by-step explanation:

4=x56×7

4=x392

392/4=X

98

6 0
3 years ago
Other questions:
  • Which expression is equivalent to 6(3+0.05)?
    6·2 answers
  • 90 minus 50 divided by 5 times 6 plus 2
    11·2 answers
  • Answer asap please...............
    5·1 answer
  • Let f(x) = 8x3 − 22x2 − 4 and g(x) = 4x − 3. Find f of x over g of x.
    12·2 answers
  • What is the volume of the cylinder
    12·2 answers
  • Find the angle with a tangent ratio of 0.6009.
    11·2 answers
  • What is the length of one leg of the triangle?<br> 9 cm<br> 972 cm<br> 18 cm<br> 18/7 cm
    5·1 answer
  • PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
    12·2 answers
  • Solve the following system of equations.
    7·1 answer
  • HELP PLEASE ME <br> I WILL GIVE BRAINLIEST
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!