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3 years ago

If the parent function is y = 1/x, describe the change in the equation y = 1/(x+4)

Mathematics

1 answer:

Ulleksa [173]3 years ago

8 0

f(x) + n - shift a graph n units up

f(x) - n - shift a graph n units down

f(x + n) - shift a graph n units left

f(x - n) - shift a graph n units right

-------------------------------------

We have:

$y=\dfrac{1}{x}\to y=\dfrac{1}{x+4}\\\\f(x)=\dfrac{1}{x}\to f(x+4)=\dfrac{1}{x+4}$

<h3>Answer: a) Moves 4 units to the left</h3>

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nter an equation and an answer to the following question: What is the original list price if the discount is $25 and the discoun

castortr0y [4]

Let us set up an equation, to determine the list price. X represents the original price

.12 * x = 25

In order to solve for X, you must divide .12 from both sides

x = 25/.12

After you divide, you should get the number 208.33

25/.12 = 208.33

So, the original list price is $208.33

7 0

3 years ago

Read 2 more answers

How to find restrictions for x?? 3. F(x)=2 sqrt x-4

stealth61 [152]

Answer:

none
none
x ≥ 4

Step-by-step explanation:

The restrictions placed on the independent variable in a function are those necessary to ensure that the function is defined for all allowed values of that variable.

In the graphs of problems 1) and 2), we see that the functions are defined for all values of x, so there are no restrictions.

3. For the function ...

$f(x)=2\sqrt{x-4}$

the value under the radical cannot be negative. The square root function is not defined for negative values, so the restriction is ...

x -4 ≥ 0

x ≥ 4 . . . . . . . add 4 to both sides of the inequality

4 0

3 years ago

A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours

qaws [65]

Answer:

The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.

Below are all the steps explained in detail.

The graph is attached.

Explanation:

1. Name the variables:

x: number of smaller lifts
y: number of larger lifts

2. Build a table to determine the number of hours each lift requires from each department:

Number of hours

small lift large lift total per department

Welding department 1x 3y x + 3y

Packaging department 2x 1y 2x + y

3. Constraints

150 hours available in welding: x + 3y ≤ 150
120 hours available in packaging: 2x + y ≤ 120
The variables cannot be negative: x ≥ 0, and y ≥ 0

Then you must:

draw the lines and regions defined by each constraint
determine the region of solution that satisfies all the constraints
determine the vertices of the solution region
test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

4. Graph

See the graph attached.

Here is how you draw it.

x + 3y ≤ 150
draw the line x + 3y = 150 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

2x + y ≤ 120
draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

the solution region is the intersection of the regions described above.

take the points that are vertices inside the solutoin region.

5. Test the profit function for each vertex

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

(0,0)
(0,50)
(42,36)
(60,0)

The profits with the vertices are:

P(0,0) = 0
P(0,50) = 25(0) + 90(50) = 4,500
P(42,36) = 25(42) + 90(36) = 4,290
P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

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3 years ago

An architect wants to draw a rectangle with a diagonal of 13 centimeters. The length of the rectangle is to be 3 centimeters mor

butalik [34]

Answer:

The rectangle is 3.2 cm by 12.6 cm

Step-by-step explanation:

See attached image for a diagram.

Choose w to represent the width because the length is described by referring to the width: it's 3 more than (add 3) triple (multiplied by 3) the width.

Length = 3w + 3

The diagonal forms two right triangles, each with leg = w, other leg = 3w + 3, hypotenuse = 13.

The Pythagorean Theorem says $(\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2$ so

$w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\$

Now solve using the Quadratic Formula with $a=5,\,b=9,\,c=-80$ .

$w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2$

The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.

5 0

3 years ago

What is the inverse of the function f(x) = 2x + 1?

alina1380 [7]

(x) = x – 2inverse of the function

8 0

3 years ago