All categories

3 years ago

Is the following relation a function?

Mathematics

1 answer:

dimulka [17.4K]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

A function is any graph that the x values do not repeat.

You can check this by using this vertical line test

Run your finger or a pencil down a specific vertical (top to bottom) line on the graph, if you can see that it intersects into the graph more than once, then it's not a function.

You might be interested in

Find the correct classisication irratinal number rational number whole number intergers

elena-s [515]

Step-by-step explanation:

Real numbers include:

Rational numbers include

Fractions, Integers

Integers include

Negative Integers, Whole numbers

Whole numbers include

Zero, Natural number

Irrational numbers

6 0

3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

4 years ago

What is the area of the composite figure?<br> (Attached picture)<br><br> __cm²

lara31 [8.8K]

Answer:

59.5

Step-by-step explanation:

area of the triangle is (7 x 3)/2=21/2=10.5

area of the square 7x7=49

7 0

3 years ago

If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v − u?

shusha [124]

Answer:

See the attached figure.

Given:

u = (-3.5 , -1.5) and v = (-1.25 , 2.25)

So,

2v = 2 * (-1.25 , 2.25) = (-2.5, 4.5)

∴ 2v - u = (-2.5, 4.5) - (-3.5 , -1.5) = (1 , 6)

The graph of the vectors is as shown in the attached figure.

8 0

3 years ago

What is the probability of rolling a five on the first die and a one

Ulleksa [173]

Answer:

The probability is 1216 chance, which is approximately a 0.46% chance

6 0

3 years ago