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4 years ago

How to determine the domain and range of a rational function?

1 answer:

5 0

The domain is essentially what x can equal, so unless there's a square root (where x has to be positive as anything squared is positive) or division (in division, the denominator can't be 0) you should be good for the most part. For the range, it's what y (the output) can equal, so I'd suggest getting the domain then figuring out what the highest and lowest y points are (as well as if y can't be anything)

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9/11=?/22 A.12 B.4 C.9 D.18

Yanka [14]

9/11 is equal to 18/22, so then D.

8 0

4 years ago

when he saw 9 customers walk in. He already had 31 wings cooked, but started cooking 32 more. The customers bought all the wings

Licemer1 [7]

Answer:

Step-by-step explanation:

31 Wings (already cooked)

+ 32 Wings (started cooking)

= 63 Wings total

divided by 9 customers

= 7 per person

8 0

3 years ago

Write an equation for the line passing through the given point and having the given slope.

Nadusha1986 [10]

Answer: The equation, in "slope-intercept form" ; is:

________________________________________________

→ " y = x + 4 " .

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Step-by-step explanation:

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Use the formula for linear equations; written in "point-slope format" ;

which is:

y − y₁ = m( x − x₁ ) ;

We are given the slope, "m" ; has a value of: "1 " ;

that is; " m = 2 " .

________________________________________________

We are given the coordinates to 1 (one) point on the line; in which the coordinates are in the form of :

" ( x₁ , y₁ ) " ;

→ that given point is: "(10, 6)" ;

in which: x₁ = 10 ;

y₁ = 6 .

→ Given: The slope, "m" equals "1" ; ________________________________________________

Let's plug our known values into the formula:

→ " y − y₁ = m( x − x₁ ) " ;

_______________________________________________

→ As follows:

→ " y − 10 = 1(x − 6) ;

______________________________________________

Now, focus on the "right-hand side of the equation" ;

→ 1(x − 6) = ? ; Simplify.

______________________________________________

Note the "distributive property" of multiplication:

→ a(b + c) = ab + ac ;

As such: " 1(x − 6) = (1*x) + (1 * -6) " ;

= 1x + (-6) ;

= x − 6 ;

[Note that: " 1 x = 1 * x = x " ;

[Note that " + (-6) " = " ( " − 6 " ) .] ;

→ {since: "Adding a negative" is the same as:

"subtracting a positive."} ;

________________________________________________

Now, let us bring down the "left-hand side of the equation" ; &

rewrite the entire equation; as follows:

________________________________________________

→ " y − 10 = x − 6 " ;

________________________________________________

Note: We want to rewrite the equation in "slope-intercept form" ;

that is; " y = mx + b " ;

in which: "y" ; stands alone as a single variable on the "left-hand side" of the equation; with "no coefficients" [except for the "implied coefficient" of " 1 "} ;

"m" is the coefficient of "x" ;

and the "slope of the line" ;

Note that "m" may be a "fraction or decimal" ; and may be "positive or negative.

If the slope is "1" ; (that is "1 over 1" ; or: " $\frac1}{1}$ " ;

then, " m = 1 " ; and we can write " 1x " as simply "x" ; since the implied coefficient is "1" ;

→ since " 1" , multiplied by any value {in our case, any value for "x"} , equals that same value.

________________________________________________

"b" refers to the "y-intercept" of the graph of the equation;

that is; the "y-value" of the point at which the graphed line of the equation crosses the "y-axis" ;

that is, the "y-value" of the coordinates of the point at which the graphed line of the equation crosses the "y-axis" ;

that is, the ["y-value" of the] y-intercept" .

Note that the value of "b" may be positive or negative, and may be a decimal or fraction.

If the value for "b" is negative, the equation can be written in the form:

" y = mx - b " ;

{since: " y = mx + (-b) " is a bit tedious .}

If the y-intercept is "0" ; (i.e. the line crosses the y-axis at the origin, at point: " (0,0) " ;

then we simply write the equation as: "y = mx " ;

________________________________________________

So; we have: → " y − 10 = x − 6 " ;

________________________________________________

→ We want to rewrite our equation in slope-intercept form,

that is; " y = mx + b " ; as explained above.

We can add "10" to each side of the equation ; to isolation the "y" on the "left-hand side" of the equation:

→ " y − 10 + 10 = x − 6 + 10 " ;

to get:

→ " y = x + 4 " ;

________________________________________________

→ which is our answer.

________________________________________________

Note: This answer: " y = x + 4 " ;

→ is written in the "slope-intercept format";

→ " y = mx + b " ;

in which: "y" is isolated as a single variable on the "left-hand side of the equation" ;

The slope of the equation is "1" ; or an implied value of "1" ;

that is; " m = 1 " ;

"b = 4 " ;

→ {that is; the "y-value" of the "y-intercept" — "(0, 4)" — of the graph of the equation is: "4 ".} .

________________________________________________

Hope this answer is helpful!

Best wishes to you in your academic pursuits

— and within the "Brainly" community!

________________________________________________

6 0

3 years ago

PLEASE ANSWER ILL CASH APP SOMEONE 10 IF THEY DO THIS WHOLE WORKSHEET FOR ME!!!

andrew-mc [135]

This is probably a scam dont listen

8 0

3 years ago

The ratio of boys to girls is 14:17 if there are 186 people altogether how many bows are in the camp

Serggg [28]

boys = 14x
girls = 17x

14x + 17x = 186
31x = 186
x = 186/31
x = 6

boys = 14x = 14 * 6 = 84

4 0

4 years ago