All categories

3 years ago

Compare the graphs of the inverse variations. y=1/x and y=2.5/x

Mathematics

1 answer:

stellarik [79]3 years ago

7 0

Answer:

The graph of

$y = \frac{2.5}{x}$

us a vertical stretch of the graph of

$y = \frac{1}{x}$

by a factor of 2.5.

Step-by-step explanation:

The given functions are

$y = \frac{1}{x}$

and

$y = \frac{2.5}{x}$

The graph of

$y = \frac{1}{x}$

is the parent rational function.

The graph of

$y = \frac{2.5}{x}$

is a vertical stretch of the parent rational function by a factor of 2.5

You might be interested in

Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect

Minchanka [31]

Answer:

<h2>Hi there !</h2>

Step-by-step explanation:

Question :- Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

Solution :-

Let the 1st paycheck be x (integer).

Mrs. Rodger got a weekly raise of $ 145.

So after completing the 1st week she will get $ (x+145).

Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.

= $ (x + 145 + 145)= $ (x + 290)

So in this way end of every week her salary will increase by $ 145.

Hope it helps u......

Stay safe, stay healthy and blessed

Have a good day !

Thank you!

5 0

3 years ago

What is 25.0996 rounded to the nearest thousandth

madreJ [45]

Answer:

25.100

Step-by-step explanation:

The thousandth place is the third digit to the right of the decimal point - tenths is the first, hundredths is the second, thousandths is the third. Since six rounds up and both nines round up, one must round up all of the way from the fourth decimal place to the tenth decimal place.

4 0

3 years ago

5. Two adjacent, supplementary angles form

marissa [1.9K]

Answer:

linear pair

Step-by-step explanation:

please follow me

7 0

2 years ago

The ratio of nickles, dimes, and quarters in a jar is 3 : 4 : 7 respectively. If there are total 112 coins in a jar how many of

jasenka [17]

Step-by-step explanation:

Nickels = 112 * 3 / (3 + 4 + 7) = 24.

4 0

3 years ago

Read 2 more answers

Can someone please help me with this? i still have 2 more pages to do and I'm stressed out of my mind I honestly just wanna pass

melisa1 [442]

1. First we are going to find the vertex of the quadratic function $f(x)=2x^2+8x+1$ . To do it, we are going to use the vertex formula. For a quadratic function of the form $f(x)=ax^2+bx +c$ , its vertex $(h,k)$ is given by the formula $h= \frac{-b}{2a}$ ; $k=f(h)$ .

We can infer from our problem that $a=2$ and $b=8$ , sol lets replace the values in our formula:
$h= \frac{-8}{2(2)}$
$h= \frac{-8}{4}$
$h=-2$

Now, to find $k$ , we are going to evaluate the function at $h$ . In other words, we are going to replace $x$ with -2 in the function:
$k=f(-2)=2(-2)^2+8(-2)+1$
$k=f(-2)=2(4)-16+1$
$k=f(-2)=8-16+1$
$k=f(-2)=-7$
$k=-7$
So, our first point, the vertex $(h,k)$ of the parabola, is the point $(-2,-7)$ .

To find our second point, we are going to find the y-intercept of the parabola. To do it we are going to evaluate the function at zero; in other words, we are going to replace $x$ with 0:
$f(x)=2x^2+8x+1$
$f(0)=2(0)^2+(0)x+1$
$f(0)=1$
So, our second point, the y-intercept of the parabola, is the point (0,1)

We can conclude that using the vertex (-2,-7) and a second point we can graph $f(x)=2x^2+8x+1$ as shown in picture 1.

2. The vertex form of a quadratic function is given by the formula: $f(x)=a(x-h)^2+k$
where
$(h,k)$ is the vertex of the parabola.

We know from our previous point how to find the vertex of a parabola. $h= \frac{-b}{2a}$ and $k=f(h)$ , so lets find the vertex of the parabola $f(x)=x^2+6x+13$ .
$a=1$
$b=6$
$h= \frac{-6}{2(1)}$
$h=-3$
$k=f(-3)=(-3)^2+6(-3)+13$
$k=4$

Now we can use our formula to convert the quadratic function to vertex form:
$f(x)=a(x-h)^2+k$
$f(x)=1(x-(-3))^2+4$
$f(x)=(x+3)^2+4$

We can conclude that the vertex form of the quadratic function is $f(x)=(x+3)^2+4$ .

3. Remember that the x-intercepts of a quadratic function are the zeros of the function. To find the zeros of a quadratic function, we just need to set the function equal to zero (replace $f(x)$ with zero) and solve for $x$ .
$f(x)=x^2+4x-60$
$0=x^2+4x-60$
$x^2+4x-60=0$
To solve for $x$ , we need to factor our quadratic first. To do it, we are going to find two numbers that not only add up to be equal 4 but also multiply to be equal -60; those numbers are -6 and 10.
$(x-6)(x+10)=0$
Now, to find the zeros, we just need to set each factor equal to zero and solve for $x$ .
$x-6=0$ and $x+10=0$
$x=6$ and $x=-10$

We can conclude that the x-intercepts of the quadratic function $f(x)=x^2+4x-60$ are the points (0,6) and (0,-10).

4. To solve this, we are going to use function transformations and/or a graphic utility.
Function transformations.
- Translations:
We can move the graph of the function up or down by adding a constant $c$ to the y-value. If $c\ \textgreater \ 0$ , the graph moves up; if $c\ \textless \ 0$ , the graph moves down.

- We can move the graph of the function left or right by adding a constant $c$ to the x-value. If $c\ \textgreater \ 0$ , the graph moves left; if $c\ \textless \ 0$ , the graph moves right.

- Stretch and compression:
We can stretch or compress in the y-direction by multiplying the function by a constant $c$ . If $c\ \textgreater \ 1$ , we compress the graph of the function in the y-direction; if $0\ \textless \ c\ \textless \ 1$ , we stretch the graph of the function in the y-direction.

We can stretch or compress in the x-direction by multiplying $x$ by a constant $c$ . If $c\ \textgreater \ 1$ , we compress the graph of the function in the x-direction; if $0\ \textless \ c\ \textless \ 1$ , we stretch the graph of the function in the x-direction.

a. The $c$ value of $f(x)$ is 2; the $c$ value of $g(x)$ is -3. Since $c$ is added to the whole function (y-value), we have an up/down translation. To find the translation we are going to ask ourselves how much should we subtract to 2 to get -3?
$c+2=-3$
$c=-5$

Since $c\ \textless \ 0$ , we can conclude that the correct answer is: It is translated down 5 units.

b. Using a graphing utility to plot both functions (picture 2), we realize that $g(x)$ is 1 unit to the left of $f(x)$

We can conclude that the correct answer is: It is translated left 1 unit.

c. Here we have that $g(x)$ is $f(x)$ multiplied by the constant term 2. Remember that We can stretch or compress in the y-direction (vertically) by multiplying the function by a constant $c$ .

Since $c\ \textgreater \ 0$ , we can conclude that the correct answer is: It is stretched vertically by a factor of 2.

4 0

3 years ago