5x -6 = 3x would be this word problem in equation form
Answer:
Shift 4 units down: ![g(x) = 2x - 10](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20-%2010)
Stretching f(x) by 4 : ![g(x) =8x - 24](https://tex.z-dn.net/?f=g%28x%29%20%3D8x%20-%2024)
Shift 4 units left: ![g(x) = 2x - 14](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20-%2014)
Compress by 1/4 units : ![g(x) = 8x - 6](https://tex.z-dn.net/?f=g%28x%29%20%20%3D%208x%20-%206)
Step-by-step explanation:
Given
![f(x) = 2x - 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%20-%206)
Required
Match the transformations (See attachment)
<u>Shift 4 units down</u>
Shifting down a function is represented as:
![g(x) = f(x) - b](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%29%20-%20b)
In this case:
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
Substitute expression for f(x) and 4 for b in ![g(x) = f(x) - b](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%29%20-%20b)
![g(x) = 2x - 6 - 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20-%206%20-%204)
![g(x) = 2x - 10](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20-%2010)
<u>Stretching f(x) by 4 </u>
Stretching a function by some units is represented as:
![g(x) =b.f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3Db.f%28x%29)
In this case:
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
Substitute expression for f(x) and 4 for b in ![g(x) =b.f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3Db.f%28x%29)
![g(x) =4 * (2x - 6)](https://tex.z-dn.net/?f=g%28x%29%20%3D4%20%2A%20%282x%20-%206%29)
![g(x) =8x - 24](https://tex.z-dn.net/?f=g%28x%29%20%3D8x%20-%2024)
<u>Shift 4 units left</u>
Shifting a function to the left is represented as:
![g(x) = f(x - b)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%20b%29)
In this case:
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
Substitute expression for f(x) and 4 for b in ![g(x) = f(x - b)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%20b%29)
![g(x) = f(x-4)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x-4%29)
Calculating f(x - 4)
![f(x) = 2x - 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%20-%206)
![f(x - 4) = 2(x - 4) - 6](https://tex.z-dn.net/?f=f%28x%20-%204%29%20%3D%202%28x%20-%204%29%20-%206)
![f(x - 4) = 2x - 8 - 6](https://tex.z-dn.net/?f=f%28x%20-%204%29%20%3D%202x%20-%208%20-%206)
![f(x - 4) = 2x - 14](https://tex.z-dn.net/?f=f%28x%20-%204%29%20%3D%202x%20-%2014)
Hence:
![g(x) = 2x - 14](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20-%2014)
<u>Compress by 1/4 units </u>
This means that the function is stretched by ![1/\frac{1}{4}](https://tex.z-dn.net/?f=1%2F%5Cfrac%7B1%7D%7B4%7D)
Compressing a function is represented as:
![g(x) =f(bx)](https://tex.z-dn.net/?f=g%28x%29%20%3Df%28bx%29)
In this case:
![b = 1/\frac{1}{4}](https://tex.z-dn.net/?f=b%20%3D%201%2F%5Cfrac%7B1%7D%7B4%7D)
![b = 1 * \frac{4}{1}](https://tex.z-dn.net/?f=b%20%3D%201%20%2A%20%5Cfrac%7B4%7D%7B1%7D)
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
Substitute expression for f(x) and 4 for b in ![g(x) =f(bx)](https://tex.z-dn.net/?f=g%28x%29%20%3Df%28bx%29)
![g(x) =f(4x)](https://tex.z-dn.net/?f=g%28x%29%20%3Df%284x%29)
Calculating f(4x)
![f(4x) = 2(4x) - 6](https://tex.z-dn.net/?f=f%284x%29%20%3D%202%284x%29%20-%206)
![f(4x) = 8x - 6](https://tex.z-dn.net/?f=f%284x%29%20%3D%208x%20-%206)
Hence:
![g(x) = 8x - 6](https://tex.z-dn.net/?f=g%28x%29%20%20%3D%208x%20-%206)
Answer:
2/3
Step-by-step explanation:
Not counting the line 4 is on, count the lines until you get to 5.
There are 3 lines.
The <em>W</em><em> </em>is on the second one.
So that's 2 out of 3 or <em>2</em><em>/</em><em>3</em><em>.</em>
Answer:
No, A
Step-by-step explanation:
Relfexive property refers to a mirror. It is a same side or angle shared by two figures.
Answer: 1.61
==================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(J) = IK/IJ
tan(J) = 45/28
tan(J) = 1.60714 approximately
tan(J) = 1.61