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11 months ago

F(x)=x-7; vertical stretch of 3 g(x)

Mathematics

1 answer:

marissa [1.9K]11 months ago

7 0

The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:

g(x) = 3x - 21.

<h3>How are vertical stretches and compression applied to the graph of a function f(x)?</h3>

Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:

g(x) = a x f(x).

Then the value of the constant determines if it is an stretch or a compression.

If the absolute value of the constant a is <u>greater than 1</u>, it is a stretch.

If the absolute value of the constant a is <u>less than 1</u>, it is a compression.

For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:

a = 3.

Then the definition of function g(x) is given by:

g(x) = 3f(x)

g(x) = 3(x - 7)

g(x) = 3x - 21.

More can be learned about transformations of functions at brainly.com/question/28810470

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malfutka [58]

Pay attention in math class! in higher grade levels, this is gonna show up EVERYDAY! no joke
In these types of problems, you need to use PEMDAS also.

((4)+3)+(13(-2)-5)
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3 years ago

Place the following steps in order to describe how to solve the following equation?!

vladimir1956 [14]

1) distribute 2 to each term within the parentheses

2) combining like terms ( which means subtract a 6-2)

3) subtract 4 from both sides of the equation

4) divide both sides of the equation by 4

Final answer should be ( x = 1/4 )

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3 years ago

In 1986, the worst nuclear disaster occurred in Chernobyl, USSR, when an explosion at a nuclear power plant released 1000 kg of

Lostsunrise [7]

Considering the function for the remaining amount of cesium in the atmosphere, F(x) = 1000×0.5^(x/30), we have;

First part:

The area will be safe again in about 100 years time.

Second part;

The y-intercept is at the start of the measurement

Third part;

The function is a decay function

<h3>Which method can be used to evaluate the given function?</h3>

First part;

The given function for the remaining amount of cesium is presented as follows;

$F(x) = 1000 \times {0.5}^{ \frac{x}{30} }$

When 100 kg. of cesium is remaining, we have;

$100= 1000 \times {0.5}^{ \frac{x}{30} }$

Which gives;

$\frac{x}{30} = \frac{ log(0.1) }{ log(0.5) }$

$x= \frac{ log(0.1) }{ log(0.5) } \times 30 \approx 100$

Therefore, the area will be safe again in approximately 100 years.

Second part;

The y-intercept is given by the point where <em>x </em>= 0

At the y-intercept, we therefore have;

$F(0) = 1000 \times {0.5}^{ \frac{0}{30} }$

F(0) = 1000

At the y-intercept, the amount of cesium remaining, F(x) is 1,000, which is the initial amount of cesium.

The y-intercept is therefore, at the start of the measurement, where 1000 kg. is present in the atmosphere.

Third part;

The amount of cesium remaining F (x) decreases as the time, <em>x</em>, increases, the function is therefore a decay function.

Learn more about exponential functions here;

brainly.com/question/2456547

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8 0

1 year ago

Find the surface area of the<br> rectangular prism.<br> 2 cm<br> 6 cm<br> 3 cm<br> [?] sq cm

Vadim26 [7]

Answer:

Step-by-step explanation:

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2 years ago

If it takes 5/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses?

saul85 [17]

Answer:

Improper Fraction: 20/3 yards

Mixed number: 6 2/3

Step-by-step explanation:

If 1 dress needed 5/6 yards to complete

then 8 dress needed

8 x 5/6 yards

which is 20/3 yards

I hope this helps

8 0

2 years ago