Functions are used to represent graphs, and vice versa.
The function represented by the graph is ![f(x) =- |x + 4| + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D-%20%7Cx%20%2B%204%7C%20%2B%203)
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
![f(x) =a |x - h| + k](https://tex.z-dn.net/?f=f%28x%29%20%3Da%20%7Cx%20-%20h%7C%20%2B%20k)
Where
![Vertex = (h,k)](https://tex.z-dn.net/?f=Vertex%20%3D%20%28h%2Ck%29)
The vertex is the minimum or the maximum point on the graph.
So, we have:
![Vertex = (-4,3)](https://tex.z-dn.net/?f=Vertex%20%3D%20%28-4%2C3%29)
The function becomes
![f(x) =a |x + 4| + 3](https://tex.z-dn.net/?f=f%28x%29%20%3Da%20%7Cx%20%2B%204%7C%20%2B%203)
The function also passes through the point (-1,0).
So, we have:
![0 =a |-1 + 4| + 3](https://tex.z-dn.net/?f=0%20%3Da%20%7C-1%20%2B%204%7C%20%2B%203)
![0 =a |3| + 3](https://tex.z-dn.net/?f=0%20%3Da%20%7C3%7C%20%2B%203)
Remove the absolute bracket
![0 =3a + 3](https://tex.z-dn.net/?f=0%20%3D3a%20%2B%203)
Subtract 3 from both sides
![3a =- 3](https://tex.z-dn.net/?f=3a%20%3D-%203)
Divide both sides by 3
![a =- 1](https://tex.z-dn.net/?f=a%20%3D-%201)
Substitute -1 for (a) in ![f(x) =a |x + 4| + 3](https://tex.z-dn.net/?f=f%28x%29%20%3Da%20%7Cx%20%2B%204%7C%20%2B%203)
![f(x) =- |x + 4| + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D-%20%7Cx%20%2B%204%7C%20%2B%203)
Hence, the function represented by the graph is ![f(x) =- |x + 4| + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D-%20%7Cx%20%2B%204%7C%20%2B%203)
Read more about absolute value graphs at:
brainly.com/question/3381225
That would be rolling a 1 and a 2 .
so possibilities are 1 on first die and 2 on the second die
OR 2 on first die and 1 on the second.
Both of these have a probability of 1/6 * 1/6 = 1/36
so required probability = 1/36 + 1/36 = 2/36 = 1/18
Answer:
Is your teacher trying to confuse us or what?
Step-by-step explanation:
well 3/3 is full so it's just like 12/12, so 12 pieces of 1/12 piece are in 3/3
Answer:
4 ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
The additive inverse is the value that must be added to the number to give zero.
- 4
+ 4
= 0
↑ additive inverse
Input data
Price model rocket = $24
Tax = $1.92
What is the percent of sales tax?
Procedure
r = percent of sales tax
![r=\frac{1.92}{24}=0.08=8\text{ \%}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1.92%7D%7B24%7D%3D0.08%3D8%5Ctext%7B%20%5C%25%7D)
The answer would be 8%