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2 years ago

Let f(x) = x^2 +3.

Mathematics

2 answers:

goblinko [34]2 years ago

7 0

Answer:

It is translated left 6 units

Step-by-step explanation:

I will help you understand graphing a function.

1. Each part in the equation represents how the graph will look.

In the first equation you have an $x^{2}$ and the number 3.

In the second equation you have an $(x + 6)^{2}$ and that same number 3.

2. First look at the variable: the $x^{2}$ tells us that both of these functions are positive quadratics opening up

3. The number on the outside tells you where the function is located on the y-axis (vertical movement)

Both equations have the number 3 so the graph will be 3 units high

4. The number on the inside with the variable determines the horizontal movement of the graph

The second equation has a (x + 6)

It might be confusing to think that since its addition the graph should go to the right but it actually goes to the left.

A good saying, I keep in my head is that parenthesis lie (x + 6) really mean 6 units to the

I will also add an image of the graph of the function below.

Sauron [17]2 years ago

3 0

Answer:

translated left by 6 units

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then shift left of a units

• If a < 0 then shift right by a units

g(x) = (x + 6)² + 3

Indicating a shift of f(x) to the left by 6 units

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Name 6 elements of PQR.

icang [17]

Answer:

josh

rabeesh

ronger

roger

roge

robert

Step-by-step explanation:

5 0

2 years ago

in solving the equation for x to distribute a minus 4 on one side of the equation what needs to be done on the other side of the

IrinaVladis [17]

The distributive property is a simplification rule that does not change the value of an expression. Nothing need be done to the other side of the equation.

q = -4(3+x)
q = -4*3 -4*x . . . . . the -4 is distributed. The right side has not changed value.

6 0

2 years ago

Read 2 more answers

What percent of increase for a population that changed from 25,000 to 30,000

tiny-mole [99]

percent of increase for a population that changed from 25,000 to 30,000

Increase in population = 30,000 - 25,000 = 5000

So, the increase in population is 5000

To find percent of increase , we divide the increase in population by initial population.

So percent of increase = $\frac{5000}{25000}$ * 100

= 0.2 * 100

= 20 %

20% of increase for a population that changed from 25,000 to 30,000.

7 0

2 years ago

Read 2 more answers

Hal and Renee play the following game a bag has 11 tiles in it each with a letter from the word probably in it Hal and Renee tak

Masteriza [31]

Answer:

<em>D. The game is not fair because the probability of Hal drawing a winning letter is less then the probability of Renee drawing a winning letter </em>

Explanation:

The word is not probably, which has 8 letters, but probability, which has 11 letters

<u>1. Hal</u>

Probability of drawing a vowel

The vowels are: o, a, i, i, and y: 5

The total number of letters in the bag is 11.

Probability of vowel = 5 / 11

<u>2. Renee</u>

Probability of drawing a consonant

The consonants are: p, r, b, b, l, t, and y: 7

Probability of a drawing a consonant: 7 /11

<h2>Conclusion</h2>

As you see, the probability of drawing a vowel (5/11), which is the winning letter for Hal, is less than the probability of drawing a consonant (7/11), which is the winning letter of Renee. Then,

The game is not fair because the probability of Hal drawing a winning letter is less then the probability of Renee drawing a winning letter.

8 0

3 years ago

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

3 0

2 years ago