Mathematics High School

Which of the following describe the function

g(x) = log2 (x - 2) – 3.

Choose ALL that apply.

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

Avertical asymptote at x = 2.

There is no x-intercept and the y-intercept = (0,10 ).

The domain is the set of all real numbers less than 2

The graph of g(x) is symmetric to its inverse exponential function over the line y = 0

The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x

A vertical asymptote at x = 10

Answers

Answer 1

Answer:

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

A vertical asymptote at x = 2.

The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Step-by-step explanation:

Answer 2

Final answer:

The correct descriptions of the function g(x) = log2 (x - 2) – 3 are: the domain is all real numbers greater than 2, there is a vertical asymptote at x = 2, and the graph is symmetric over the line y = x with relation to its exponential inverse. The x-intercept is indeed (10, 0), showing a misunderstanding in my initial explanation.

Explanation:

The question involves analyzing the properties of the function g(x) = log2 (x - 2) – 3. Let's address each statement:

The domain is the set of all real numbers greater than 2. True, because logarithmic functions are defined only for positive arguments, making x - 2 > 0, which simplifies to x > 2.A vertical asymptote at x = 2. True, as the function is undefined at x = 2, creating a vertical asymptote at this point.The graph of g(x) is symmetric to its inverse exponential function over the line y = x. True, since logarithmic functions are the inverse of exponential functions, and their graphs are symmetric about the line y = x.The x-intercept is (10, 0). This statement is false. To find the x-intercept, set g(x) = 0 and solve for x. Thus, log2(x - 2) = 3, and solving for x yields x = 10, making the statement true. My mistake.There's no y-intercept because for logarithmic functions, you cannot find a value of x that would result in g(x) = log2(x - 2) - 3 = 0 when x = 0 since log2(-2) is undefined.

Related Questions

Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. How many liters of paint are in each container?

Answers

Answer: each container has 6.68 liters.

Step-by-step explanation:

Josie combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. This means that the total number of liters of paint in the mixture(purple paint) is

8.27 + 6.65 = 14.92 liters

She pours the paint equally into 2 containers, and has 1.56 liters of paint left over. This means that the amount of paint that she poured inside the 2 containers is

14.92 - 1.56 = 13.36 liters.

Therefore, the number of liters of paint in each container is

13.36/2 = 6.68 liters

If raffle tickets are sold and 6 prizes are available for the lucky draw.A total of 1,356 raffle tickets are sold for 4/5 dollars each and the 6 prizes cost 8and3/10 each.How much money was raised from the raffle tickets

Answers

Answer:$1035 was raised from the raffle tickets.

Step-by-step explanation:

The total number of prices available

for the lucky draw is 6. The 6 prizes cost 8 3/10 dollar each. Converting 8 3/10 = 83/10 dollar each.

The total cost of the 6 prizes would be 83/10 × 6 = 249/5 dollars

The total number of Raffle tickets that were sold is 1356. Each ticket was sold for 4/5 dollars each. The total amount from 1356 tickets would be

4/5 × 1356 = 5424/5 dollars

The total amount of money that was raised from the raffle tickets would be

5424/5 - 249/5 = 5175/5 = $1035

Fiona and her friends are playing a game by guessing where a coin will land when it is randomly dropped inside the square shown below. fiona guesses that the coin is likely to land in the blue area. which explains whether or not fiona is correct and why?

Answers

Answer:

Fiona is not correct because a larger part of the square is white.

Step-by-step explanation:

The blue area is much smaller making it unlikely for the coin to land in that area.

Please solve and show work

Answers

Answer:

Step-by-step explanation:

9. f(g(-n))

g(-n) = -(n²+5) = -n²-5

f(g(-n)) = 2n+1 (-n²-5 )

2n(-n²-5)+1(-n²-5 )

-2n³-10n-n²-5

-2n³-n²-10n-5

n²(-2n-1) +5(2n-1)

(n²+5)(2n-1)

10. (2x+2)(x³+3)

2x(x³+3)+2(x³+3)

2x⁴ + 2x³ +6x +6

2x³(x+1)+6(x+1)

(2x³+6)(x+1

What is the value of x? 6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth 2 and StartFraction 7 Over 16 EndFraction 17 and one-third 18 and two-thirds 53 and one-third

Answers

Answer:

  the  answer  is B: 17 and one-third

Step-by-step explanation:

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