Given the graph of y = 2x² is transformed into y = -2x² + 3.
For any function y = f(x), the transformation y' = -y = -f(x) reflects the graph across x-axis.
So it means that y = -2x² is the reflection of y = 2x² across the x-axis.
For any graph y = g(x), the transformation y' = y + k = g(x) + k shifts the graph 'k' units upward for all value of 'k' > 0.
So it means that y = -2x² + 3 is the shifted version of y = -2x² by '"3 units up".
Hence, option B and C are correct i.e. "reflection across x-axis" and "shift of 3 units up".
Answer:
The function g(x) simply takes the value x and turns it into its reciprocal value . Thus, for instance, the number 5 becomes , and becomes 2. Note that any value of x works in this function as long as is defined. As mentioned, fractions work as well as whole numbers, both for positive and negative values; the only value that does not work is 0, since is undefined (how many times can 0 go into 1?). Thus, the domain of the function is all x in where x ≠ 0. Let's look at the graph of the function also.
Step-by-step explanation:
The function f simply takes in input value x, multiplies it by 2, and then adds 3 to the result. We can therefore consider what constitutes the set of numbers that the function can accept as an input and what constitutes the set of numbers that the function can yield as an output.
Answer:
10/-3
Step-by-step explanation:
use the equation y2-y1/x2-x1
put it in
5+5/2-5
10/-3
Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:
- The probability a person wins a game is 3/8 or 37.5%.
- For a participant to win 25% of the time, they needs to get 32 or higher.
- The probability of a score of 36 or higher in 4 consecutive attempts is 1/1,1296.
- Teacher should tell people that just as the lower numbers could be picked, the products that are 32 or higher can be picked as well.
<h3>What sample space represents the data?</h3>
If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.
The sample space is:
Dice Card Product
1 5 5
1 6 6
1 7 7
1 8 8
2 5 10
2 6 12
2 7 14
2 8 16
3 5 15
3 6 18
3 7 21
3 8 24
4 5 20
4 6 24
4 7 28
4 8 32
5 5 25
5 6 30
5 7 35
5 8 40
6 5 30
6 6 36
6 7 42
6 8 48
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Based on the products, we can come up with the following frequency table:
Frequency table
Product Frequency
5 1
6 1
7 1
8 1
10 1
12 1
14 1
16 1
15 1
18 1
21 1
24 2
20 1
28 1
30 2
32 1
25 1
35 1
40 1
36 1
42 1
<u>48 1</u>
<u>Total 24</u>
The frequency table shows that to get 28 or more, a person will have a relative frequency of:
= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1
= 9
Probability is:
= 9 / 24
= 3/8
= 37.5%
<h3>How can a person win only 25% of the time?</h3>
The number of products required to win 25% of the time is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
<h3 /><h3>What is the probability that a player wins a large prize?</h3>
The probability of getting 36 or higher is:
= ∑(Probabability of picking 36 and above numbers)
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 consecutive times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
= 0.0007716
Find out more on probability at brainly.com/question/23461431.
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Area of a rectangle is length times width:
3 to the (2 over 3) power is ∛3²
A=∛81*∛3²
A=3∛3 * ∛3²=3∛3³=3*3=9
the answer is C.