Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of ____

The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio

Anna35 [415]

Answer:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Step-by-step explanation:

As the original function is

$f(x) = \sqrt{x}$

Since, domain is the set of all possible input values that define the function, and range is the set of all possible output values for all possible domain values for which the function is defined.

The domain of $f(x) = \sqrt{x}$ will be [0, ∞)

The range of $f(x) = \sqrt{x}$ will be [0, ∞)

Please check the attached figure a for visualizing the graph of $f(x) = \sqrt{x}$ .

Impact of double transformation:

When the function $f(x) = \sqrt{x}$ is reflected across x-axis, the function becomes $y = -\sqrt{x}$ after first transformation

After the second transformation across y-axis, the function $y = -\sqrt{x}$ becomes $g(x) = -\sqrt{-x}$

For

$g(x) = -\sqrt{-x}$

$-x$ must be equal to or greater than zero for $g(x) = -\sqrt{-x}$ to be defined i.e. -x ≥ 0.

So,

-x ≥ 0 can be written as x≤ 0

So,

The domain of $g(x) = -\sqrt{-x}$ will be (∞, 0]
The range of $g(x) = -\sqrt{-x}$ will be (∞, 0]

Please check the attached figure a for visualizing the graph of $g(x) = -\sqrt{-x}$ .

So, from the above discussion, we can say that

0 is the only that is in the domain of both function.
The range of g(x) is all values less than or equal to 0

So,

Only two statements are true about the functions f(x) and g(x) are true which are:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Keywords: graph, function

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8 0

1 year ago

Read 2 more answers

The graph of the parent function f(x) = x2 is dashed and the graph of the transformed function g(x) = (x – h)2 is solid. Use the

STALIN [3.7K]

The graph of the parent function f(x) = x2 is dashed and the graph of the transformed function g(x) = (x – h)2 is solid.

If h=3 the vertex shifts to (3,0).

If h=-5 the vertex is shifted to (-5,0)

I hope this helps! Sorry no one got back to you in the past few days ):

3 0

2 years ago

Read 2 more answers

Given: circle O with tangent AB mBC= 2x -16; mCD = x+40; mDE = x; mEB = 60 find the x

murzikaleks [220]

Answer:

69

Step-by-step explanation:

All the given arcs cover the entire circle circumference, so their measures add up to a full 360.

(2x - 16) + (x + 40) + x + 60 = 360

4x + 84 = 360

4x = 276

x = 69

6 0

2 years ago

Joan is hiking. She wants to cover 1,600 feet. She hikes 600 feet every 3 hours.

Stella [2.4K]

Joan's remaining distance is reduced by (600 ft)/(3 hours) = 200 ft/hour. She starts with 1600 ft remaining, so her distance remaining (y) after x hours is
.. y = -200x +1600

In order for the distance remaining to be zero, you must have
.. 0 = -200x +1600
.. 200x = 1600
.. x = 1600/200 = 8

It will take Joan 8 hours to hike 1600 ft.

6 0

2 years ago

Which of the following gives a valid reason for using the given solution method to solve the system of equations shown? Equation

alukav5142 [94]

Answer:

* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.

* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.

Step-by-step explanation:

Equation I: 4x − 5y = 4

Equation II: 2x + 3y = 2

These equation can only be solved by Elimination method

Where to Eliminate x :

We Multiply Equation I by a coefficient of x in Equation II and Equation II by the coefficient of x in Equation I

Hence:

Equation I: 4x − 5y = 4 × 2

Equation II: 2x + 3y = 2 × 4

8x - 10y = 20

8x +12y = 6

Therefore, the valid reason using the given solution method to solve the system of equations shown is:

* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.

* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.

4 0

2 years ago

Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.