Ask question

Ask question

All categories

8 days ago

5

f(x) = 7x g(x) = 7x + 6 Which statement about f(x) and its translation, g(x), is true? The domain of g(x) is {x | x > 6}, and

the domain of f(x) is {x | x > 0}. The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}. The asymptote of g(x) is the asymptote of f(x) shifted six units down. The asymptote of g(x) is the asymptote of f(x) shifted six units up.

2 answers:

Leona [4.1K]8 days ago

7 0

The asymptote of g(x) represents the asymptote of f(x) shifted six units upwards.

Inessa [3.9K]8 days ago

5 0

Answer:

The fourth option is correct: the asymptote of g(x) is the asymptote of f(x) shifted six units upwards.

Step-by-step explanation:

The functions provided are

$f(x)=7x$

$g(x)=7x+6$

Both functions are linear, and the domain of linear functions encompasses all real numbers.

Domain of f(x) = {x | x∈R }

Domain of g(x) = {x | x∈R }

Hence, options 1 and 2 are incorrect.

The linear asymptote of a linear function $f(x)=mx+b$ is

$y=mx+b+\delta x$

Where δx is an infinitesimal number, not equal to 0.

The asymptote for f(x) is

$y=7x+\delta x$

The asymptote for g(x) is

$y=7x+6+\delta x$

This indicates that the asymptote of f(x) is raised six units upward to obtain the asymptote of g(x).

Consequently, option 4 is correct: the asymptote of g(x) is the asymptote of f(x) shifted six units upward.

You might be interested in

In three hours, Company ABC can make X ball bearings. Company DEF can make X ball bearings in 4 hours. Company GHI can make X ba

AnnZ [3900]

Answer:

X ball bearings can be produced in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

Proportions serve as an essential method for solving various common challenges. We understand that:

Company ABC manufactures X ball bearings in 3 hours.

Company DEF produces X ball bearings in 4 hours.

Company GHI generates X ball bearings in 6 hours.

In a single hour, each company is capable of producing:

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

By collaborating, they can produce

$\displaystyle \frac{X}{3}+\frac{X}{4}+\frac{X}{6}$

ball bearings. Operating together

$\displaystyle \frac{4X+3X+2X}{12}=\frac{9X}{12}=\frac{3X}{4}$

If their output is 3/4 of a ball bearing in one hour, then it will take

$\displaystyle \frac{4}{3}$ hours to create one complete ball bearing. This translates to 1 hour and 20 minutes.

X ball bearings can be produced in 1 hour and 20 minutes

8 0

17 days ago

The graph of the function f(x) = (x – 4)(x + 1) is shown below. On a coordinate plane, a parabola opens up. It goes through (neg

tester [3938]

Answer:

The function decreases across all real numbers x where x < 1.5.

Step-by-step explanation:

We have

$f(x)=(x-4)(x+1)$

$f(x)=x^2+x-4x-4$

$f(x)=x^2-3x-4$

This represents an upward-opening vertical parabola

The vertex denotes a minimum point

The vertex is located at (1.5,-6.25)

We know that

The function is decreasing within the interval ----> (-∞, 1.5) x < 1.5

This means----> the function is continuously decreasing for all real x values under 1.5

Conversely, the function is increasing within the interval ----> (1.5, ∞) x> 1.5

Thus, for all real x values greater than 1.5, the function is increasing

Check the attached figure for further clarification

Therefore

The true statement is

The function decreases across all real numbers x where x < 1.5.

5 0

6 days ago

Read 2 more answers

Julia can finish a 20-mile bike ride in 1.2 hours. Katie can finish the same bike ride in 1.6 hours. How much faster does Julia

Svet_ta [4341]

Given that, $speed = \frac{distance}{time}$

Julia completes a 20-mile bike ride in 1.2 hours.

The distance Julia covers is 20 miles and her time taken is 1.2 hours.

Therefore, Julia's speed = $\frac{20}{1.2}$ = 16.67 mph

Katie finishes the same 20-mile ride in 1.6 hours.

Katie’s distance is 20 miles and her time is 1.6 hours.

Hence, Katie's speed = $\frac{20}{1.6}$ = 12.5 mph

To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.

Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.

Consequently, Julia cycles 4.2 mph faster than Katie.

5 0

14 days ago

Read 2 more answers

A rectangular schoolyard is to be fenced in using the wall of the school for one side and 150

lawyer [4039]

Answer:

Part 1) The equation is $A(x)=150x-2x^2$

Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

$P=2x+y$

$P=150\ m$

thus

$150=2x+y$

$y=150-2x$ -----> this is equation A

The area of the rectangular school yard is

$A=xy$ ----> this is equation B

Substituting equation A into equation B yields

$A=x(150-2x)$

$A=150x-2x^2$

Change to function notation

$A(x)=150x-2x^2$

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

$A(40)=150(40)-2(40^2)$

$A(40)=2,800\ m^2$

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

$A(x)=150x-2x^2$

This forms a vertical parabola opening downwards

The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

The y-coordinate of the vertex denotes the maximum area

The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

The x-intercepts are located at x=0 m and x=75 m

The domain for A is the range -----> (0, 75)

All real numbers greater than zero and less than 75 meters

5 0

11 days ago

Adrianne jogs for 15 minutes at 6 miles per hour. How many miles does she jog?

Svet_ta [4341]

Response: 3.2

Detailed explanation:

3 0

2 days ago

Read 2 more answers