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3 years ago

Given that (5,6) is on the graph of f(x), find the corresponding point for the function 4f(x)

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

4 0

Answer:

The corresponding point for the function 4f(x) is (5 , 24)

Step-by-step explanation:

* Lets revise some transformation

- A vertical stretching: is the stretching of the graph away from

the x-axis

- A vertical compression: is the squeezing of the graph toward

the x-axis.

• if k > 1, the graph of y = k • f(x) is the graph of f (x) vertically

stretched by multiplying each of its y-coordinates by k.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

by multiplying each of its y-coordinates by k.

* In our problem:

- Point (5 , 6) is on the graph of f(x)

- The function will be 4f(x), that means vertical stretching

or vertical compression

∵ k = 4

∵ 4 > 1

∴ It is a vertical stretch

∴ We will multiply the y-coordinate by 4

∴ y' = 4 × 6 = 24

* The corresponding point for the function 4f(x) is (5 , 24)

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What is equation of the line that passes through the point (-3,8) and has an undefined slope

aniked [119]

The equation of line that passes through point (-3, 8) and has an undefined slope is x = -3

<u>Solution:</u>

Given that we have to find the equation of line that passes through point (-3, 8) and has an undefined slope

Since the line has an undefined slope. This informs us that it is a vertical line parallel to the y-axis and passing through all points in the plane with the same x-coordinate.

If the slope of the line is undefined, then, by definition the line is a vertical line.

For a vertical line, the value of x is the same for each and every value of y

Given point is (x, y) = (-3 , 8)

Because the value of x in the point provided in the problem is -3, we get

Equation of line is : x = -3

8 0

3 years ago

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone d

kompoz [17]

Answer:

The function f(x) is represented by:

$f(x)=1500(0.97)^x$

Hence, a=1500 and b=0.97

Step-by-step explanation:

The patient currently has a bone density of 1,500 kg/mg^3.

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually.

This means that the bone density that is remaining is:

100-3=97%

which is also represented as: 97%=97/100=0.97

Hence, the function f(x) that represents the bone density after x years is represented by:

$f(x)=a(0.97)^x$

where a is the initial bone density which is given to be: 1500 kg/mg^3.

Hence, the function is:

$f(x)=1500(0.97)^x$

6 0

3 years ago

Read 2 more answers

What polynomial has a graph that passes through the given points?

Evgen [1.6K]

The answer is <span>B. y = x^3 + 4x^2 + 2x - 2

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

</span>B. y = x³ + 4x²<span> + 2x - 2
Point 1: </span><span>(-2, 2)
x = -2
y = 2
____
2 = (-2)</span>³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1)
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2
-1 = -1
____

Point 3: (1, 5)
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67)
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.

3 0

3 years ago

How is the number 5 divisible into 1,620

Gennadij [26K]

-Notice that dividing our numbers leaves no remainder:

1,620 ÷ 5 = 324 + 0

-1,620 has all the factors of the number 5

7 0

3 years ago

Complete the square to the problem X^2+6x-16=0

marishachu [46]

Answer:

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}$

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3 years ago