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
Sever21 [200]
3 years ago
6

Why does a radical function with an even index only appear on one sode of the x-axis while a radical woth an odd index appears o

n both sides?
Mathematics
1 answer:
Vladimir79 [104]3 years ago
3 0

Consider the equation y = x^2. No matter what x happens to be, the result y will never be negative even if x is negative. Example: x = -3 leads to y = x^2 = (-3)^2 = 9 which is positive.

Since y is never negative, this means the inverse x = sqrt(y) has the right hand side never be negative. The entire curve of sqrt(x) is above the x axis except for the x intercept of course. Put another way, we cannot plug in a negative input into the square root function for this reason. This similar idea applies to any even index such as fourth roots or sixth roots.

Meanwhile, odd roots such as a cube root has its range extend from negative infinity to positive infinity. Why? Because y = x^3 can have a negative output. Going back to x = -3 we get y = x^3 = (-3)^3 = -27. So we can plug a negative value into the cube root to get some negative output. We can get any output we want, negative or positive. So the range of any radical with an odd index is effectively the set of all real numbers. Visually this produces graphs that have parts on both sides of the x axis.

You might be interested in
What is the volume of a cylinder? Give an informal argument for the formula.
N76 [4]
The formula to find the volume of a cylinder is 3.14 • r squared • h
3 0
3 years ago
What is slope intercept form
Nat2105 [25]
Slope intercept form is y=mx+b
4 0
3 years ago
Read 2 more answers
So I don't know to solve this <br>​
Kruka [31]

Answer:

A

Step-by-step explanation:

When a slope is undefined, it is always x = ?

The point (-5, -8) tells us that x = -5

Option A also has a point with x = -5

5 0
2 years ago
David &amp; Brad are competing in a 20-mile bicycle race. David rides 6.2 miles in 1/4 hour. Brad rides 11.9 miles in 1/2 hour.
Elodia [21]
David will finish first, because if you divide Brad's miles by 2 to his miles in a 1/4 of an hour are 5.95 miles. This means David went 6.2 miles in the same time that Brad went 5.95. Therefore, David will finish first.
6 0
3 years ago
What is the area of a figure that is formed using a parallelogram with base 5.2 meters and height 3 meters, and a semicircle wit
S_A_V [24]

Answer:

40.7m^2

Step-by-step explanation:

Base×Height= 5.2m×3=15.6m2

Area of semicircle= Pie r^2= Pie×4^2=16×pie

pie×16÷2=8×pie

8×3.14=25.12m2

15.6m2+25.12m2=40.72m2

rounded to nearest tenth=40.7m2

8 0
3 years ago
Read 2 more answers
Other questions:
  • Urgent help needed w/ right triangle trig
    8·1 answer
  • C.) In a special paint the following tints are added, 200ml of green tint,350ml of blue tint and 450ml of red tint. calculate th
    15·1 answer
  • Plis i need help whit this questionss​
    15·1 answer
  • Heights of adult males are normally distrubed. If a large sample of heights of adult males is randomly selected and the heights
    10·1 answer
  • Which students write the correct express
    7·1 answer
  • Write a sentence containing a gerund which functions as the subject of the verb.
    6·1 answer
  • Given parallelogram JKLM, complete the following statements.
    14·1 answer
  • 25 The library has an empty bookcase with 4 shelves. Each shelf can hold 23 chapter þooks. If the library has 117 new chapter bo
    15·2 answers
  • Anna is solving this equation:
    15·2 answers
  • Point M is located at (7,1).
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!