Answer:
A) ![y=-5x-4](https://tex.z-dn.net/?f=y%3D-5x-4)
B) ![y=-5x+4](https://tex.z-dn.net/?f=y%3D-5x%2B4)
C) ![y=\frac{x-4}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx-4%7D%7B5%7D)
Step-by-step explanation:
So we have the equation:
![y=5x+4](https://tex.z-dn.net/?f=y%3D5x%2B4)
Let's write this in function notation. Thus:
![y=f(x)=5x+4](https://tex.z-dn.net/?f=y%3Df%28x%29%3D5x%2B4)
A)
To flip a function over the x-axis, multiply the function by -1. Thus:
![f(x)=5x+4\\-(f(x))=-(5x+4)](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4%5C%5C-%28f%28x%29%29%3D-%285x%2B4%29)
Simplify:
![-f(x)=-5x-4](https://tex.z-dn.net/?f=-f%28x%29%3D-5x-4)
B) To flip a function over the y-axis, change the variable x to -x. Thus:
![f(x)=5x+4\\f(-x)=5(-x)+4](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4%5C%5Cf%28-x%29%3D5%28-x%29%2B4)
Simplify:
![f(-x)=-5x+4](https://tex.z-dn.net/?f=f%28-x%29%3D-5x%2B4)
C) A reflection over the line y=x is synonymous with finding the inverse of the function.
To find the inverse, switch x and f(x) and solve for f(x):
![f(x)=5x+4](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4)
Switch:
![x=5f^{-1}(x)+4](https://tex.z-dn.net/?f=x%3D5f%5E%7B-1%7D%28x%29%2B4)
Subtract 4 from both sides:
![x-4=5f^{-1}(x)](https://tex.z-dn.net/?f=x-4%3D5f%5E%7B-1%7D%28x%29)
Divide both sides by 5:
![f^{-1}(x)=\frac{x-4}{5}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx-4%7D%7B5%7D)
And we're done :)
Answer:
320m
Step-by-step explanation
a rectangle has four sides, two pairs of identical sides. So two sides are 16. So that adds up to 32. Perimeter is all sides added together. so it has to add up to 72. 72 minus 32 is 40, so two of the sides have to be 40. Area is length times width, so 16 times 20, which is 320.
Answer:
$54.50
Step-by-step explanation:
10% = 10/100
=545 × 10/100
=5450/100
=54.5
Answer:
The initial value in the word problem is the output value when input value is set to zero.
Step-by-step explanation:
- In the question, it is given that a problem uses a linear function.
- It is required to explain how to interpret the initial value in a word problem.
- In order to find the initial value in a world problem, find the output value when input value is set to zero.
- If the initial value is marked as b for a linear function f(x), find it as follow,
Answer:
y-1=5(x+6)
Step-by-step explanation:
Point slope:
(y-y1)=slope(x-x1)
y-1=5(x+6)
Hope this helps!