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tensa zangetsu [6.8K]
3 years ago
10

State the domain of the function.

Mathematics
2 answers:
alexandr402 [8]3 years ago
8 0

Answer:

The domain of the function is { -2 , 0 , 1 , 2 , 3 , 4} ⇒ 1st answer

Step-by-step explanation:

Snowcat [4.5K]3 years ago
7 0

Answer:

The domain of the function is { -2 , 0 , 1 , 2 , 3 , 4} ⇒ 1st answer

Step-by-step explanation:

* Lets explain the meaning of the function

- The function is a relation between x and y under condition of

  every x has only one value of y

Ex: The relation {(-1 , 2) , (2 , 4) , (3 , 2)} is a function because

      every x has one value of y

     The relation {(-1 , 2) , (2 , 4) , (2 , 2)} is NOT a function because

      one x has two values of y ⇒ 2 has two values of y  4 and 2

- x is the input and called the domain of the function

- y is the output and called the range of the function

* Lets solve the problem

∵ The set of points = {(-2, -4) , (0 , 0) , (1 , 1) , (2 , 2) , (3 , 1) , (4 , 6)}

- Every x has only one value of y

∴ The set of points is a function

∵ The domain of the function is the values of x

∴ The domain of the function is { -2 , 0 , 1 , 2 , 3 , 4}

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Answer:

11/19

Step-by-step explanation:

Firstly, we need to know the total number of instructors. This is equal to 7+5+4+3 = 19 instructors.

The probability of selecting a science instructor is 4/19

The probability of selecting a math instructor is 7/19

The probability of selecting either a science or a maths instructor is 4/19 + 7/19 = 11/19

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Which is the value of this expression when p = -2 and q = -1?
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The line through (-1/2, -7/2) and (2, 14) in slope intercept form??
icang [17]
To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (m):

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

We can replace the variables in this equation with the values from the points we have been given, (\frac{-1}{2},  \frac{-7}{2}) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair x_{2} and the \frac{-1}{2} in the first ordered pair x_{1}.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.

m =  \frac{y_{2}-y _{1}}{x_{2}-x_{1}}

m =  \frac{14 -  \frac{-7}{2} }{2 -  \frac{-1}{2} }

Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as

m =  \frac{14 +  \frac{7}{2} }{2 +  \frac{1}{2} }

and we can change the improper fraction in the numerator into a mixed number for ease of addition.

m =  \frac{14 + 3 \frac{1}{2} }{2+ \frac{1}{2} }

And here, we can add, since it's made simple for us.

m =  \frac{17  \frac{1}{2} }{2  \frac{1}{2} }

Finally, to get the slope we can complete the fraction by dividing.

17.5 ÷ 2.5 = 7

The slope of this equation, m, is 7, and so far, our equation looks like this:

y = 7m + b

Now, to find y-intercept.

To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.

y = 7x + b

Let us substitute in our values.

14=7(2)+b

Now, we can solve by multiplying the 7 and 2.

14=14+b

Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with

0 = b

which can be flipped around to show

b=0

The y-intercept of this line is 0.

Now, we can make this known in our equation like this:

y=7x+0

Or, for neatness' sake, we can just say

y=7x

which is your final equation.

The line through (\frac{-1}{2},  \frac{-7}{2}) and (2, 14) in slope-intercept form is <span>y=7x.
Hope that helped! =) </span>


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