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grandymaker [24]
3 years ago
10

Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretch

ing, and/or reflecting. Find the domain and range of the function. f(x) = -(x + 1)3-1

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
8 0

Answer:

Domain and range of the function is all real number.

Step-by-step explanation:

The given function is

f(x)=-(x+1)^3-1                .... (1)

It is a cubic function.

The parent cubic function is

g(x)=x^3

The translation is defined as

h(x)=k(x+a)^3+b                .... (2)

where, k is stretch factor, a is horizontal shift and b is vertical shift.

If |k|>1, then the graph of g(x) stretch by factor k and if 0<|k|<1

, then the graph of g(x) compressed by factor k. If k<0, then graph of g(x) reflects across x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2), we get

k=-1<0, so the graph reflects across x-axis.

a=1>0, so the graph of parent function shifts 1 units left.

b=-1<0, so the graph of parent function shifts 1 units down.

Domain and range of cubic polynomial is all real number. Since the given function is a cubic polynomial, therefore domain and range of the function is all real number.

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A greater fraction than 4/5 is 9/10
4 0
3 years ago
If y = 3x - 4 and the domain is {-3,-1,4}, find the range.
aivan3 [116]
3x - 4 = <span>3(-3)  - 4 = -9 - 4 = -13
</span>3x - 4 = <span>3(-1.4)  - 4 = -4.2 - 4 = -8.2

answer
range { -13, -8.2}</span>
4 0
3 years ago
The sum of Veronika's and Kate's weight is 118 pounds. Veronika weighs 26 pounds more than Kate. How much do they weigh individu
Ray Of Light [21]

Answer:

Veronika's weight = 92 pounds

Kate's weight = 46 pounds

Step-by-step explanation:

Let Veronika's weight = x

Let Kate's weight = y

The sum of Veronika's and Kate's weight is 118 pounds.

x + y = 118

Veronika weighs 26 pounds more than Kate.

x = y + 26

How much do they weigh individually?

We substitute y + 26 for x in Equation 1

x + y = 118

y + 26 + y = 118

26 + 2y = 118

2y = 118 - 26

2y = 92

y = 92/2

y = 46 pounds

x = y + 26

x = 46 + 26

x = 92 pounds

Hence,

Veronika's weight = 92 pounds

Kate's weight = 46 pounds

8 0
2 years ago
How do you solve multi variable equations?​
Mekhanik [1.2K]
1. Understand what multi-variable equations are.

Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.

2. Know that you are trying to figure out the values of the variables, or unknowns.

The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.

• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.

3. Know what a numerical coefficient is.

The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:

• 8 and 3 for the first equation; 5 and 2 for the second equation.


4. Understand the difference between solving with elimination and solving with substitution.

When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).

• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.


5. Understand that there can be linear equations that have three or more variables.

Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.
6 0
3 years ago
Minhaoh i need help go to my profile the qustion will be there no links
Ugo [173]

Answer:

Wdym

Step-by-step explanation:

3 0
3 years ago
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