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sweet [91]
3 years ago
12

Please help me with this question. Algebra 2 is hard!!

Mathematics
1 answer:
trapecia [35]3 years ago
3 0

Answer:

  • domain: {x ∈ ℝ : x ≤ 5}
  • range: {y ∈ ℝ : y ≤ -1}

Step-by-step explanation:

<u>Domain</u>

The domain of a function is the set of x values for which the function is defined. Here, the domain is limited by the values of x that make the square root defined. That is, the expression under the radical cannot be negative:

  -3x +15 ≥ 0

  15 ≥ 3x . . . . . . add 3x

  5 ≥ x . . . . . . . . divide by 3

  x ≤ 5 . . . . . . . . put x on the left (swap sides)

The rest of the notation in the domain expression simply says x is a real number.

  domain: {x ∈ ℝ : x ≤ 5} . . . . . . matches the first choice

__

<u>Range</u>

The range of a function is the set of values that f(x) can have. We know the square root can be zero or any positive number. When it is zero, f(x) = -1.

When it is a positive number, that value is multiplied by -4 and added to -1, so f(x) is a number more negative than -1. Then the range of the function is all numbers -1 and below:

  range: {y ∈ ℝ : y ≤ -1} . . . . . . matches the last choice

_____

<em>Comment on domain/range problems</em>

When working domain and range problems, it works well to have a good understanding of the domain and range limitations of the functions we usually work with: polynomials, square root, logarithm, trig functions, exponential functions. Domain and range problems generally involve combinations of these or ratios of combinations of these.

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Tcecarenko [31]

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7 0
3 years ago
when a linear function is graphed it passes through the points (-1,1), (1,5), and (3,9) what is the rate of change for the funct
vesna_86 [32]
Use the linear slope formula to solve for m: 

m=(y2-y1)/(x2-x1)

using the points (-1,1) and (1,5) you can find the slope for the first interval:
 
m=(5-1)/(1-(-1))
m=4/2
m=2

you can double check by using the same formula on the second interval, which is (1,5) to (3,9).

m=(9-5)/(3-1)
m=4/2
m=2 

therefore, the rate of change is 2. 
5 0
3 years ago
Which skier will have a greater potential energy? Skier one is higher then skier two.
masha68 [24]
Skier one will have more potential energy
7 0
3 years ago
Read 2 more answers
Find the range and interquartile range for the data represented by the box plot.
Anarel [89]

<u>Given</u>:

Given that the data are represented by the box plot.

We need to determine the range and interquartile range.

<u>Range:</u>

The range of the data is the difference between the highest and the lowest value in the given set of data.

From the box plot, the highest value is 30 and the lowest value is 15.

Thus, the range of the data is given by

Range = Highest value - Lowest value

Range = 30 - 15 = 15

Thus, the range of the data is 15.

<u>Interquartile range:</u>

The interquartile range is the difference between the ends of the box in the box plot.

Thus, the interquartile range is given by

Interquartile range = 27 - 18 = 9

Thus, the interquartile range is 9.

3 0
3 years ago
Read 2 more answers
HELP NEEDED ASAP WILL GIVE 5 STAR RATING AND BRAINLIEST!
stealth61 [152]

Answer:

The answer to your question is: ∠K   = 138°

Step-by-step explanation:

m∠N = 42°

m∠K = ?

The sum of all the internal angles in a quadrangle equals 360°

then

        ∠N + ∠L + ∠M + ∠K = 360°

        ∠N = ∠ L   and ∠M = ∠K

So, 2 ∠N + 2 ∠K = 360

Substitution

       2 (42) + 2 ∠K = 360

       84  + 2 ∠K = 360

       2 ∠K = 360 - 84

       2 ∠K = 276

      ∠K  = 276 / 2

     ∠K   = 138°

8 0
3 years ago
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