Relation 1 is a function because we don't have any repeated x values. Each input goes to exactly one output.
On the other hand, relation 2 is <u>not</u> a function because x = 4 repeats itself. The input x = 4 leads to more than one output.
4x - 1 = -4x + 1
8x - 1 = 1 (added 4x to both sides)
8x = 2 (added 1 to both sides)
x = ![\frac{2}{8} = \frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B8%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%20)
Answer: there is ONE solution
Your answer is going to be -20.
Answer:
Step-by-step explanation:
Answer:
- Parent Function:
![y=\sqrt{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%7Bx%7D)
- Horizontal shift: right 3 units
- Vertical shift: up 3 units
- Reflection about the x-axis: none
- Vertical strech: streched
Step-by-step explanation:
assume that
is
and
is
![g(x)=\sqrt{-2x+6}+3\\ f(x)=\sqrt{x} \\g(x)=\sqrt{-2x+6}+3](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%7B-2x%2B6%7D%2B3%5C%5C%20f%28x%29%3D%5Csqrt%7Bx%7D%20%5C%5Cg%28x%29%3D%5Csqrt%7B-2x%2B6%7D%2B3)
The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.
![y=a\sqrt{x-h}+k](https://tex.z-dn.net/?f=y%3Da%5Csqrt%7Bx-h%7D%2Bk)
factor a 1 out of the absolute value to make the coefficient of x equal to 1
![y=\sqrt{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%7Bx%7D)
factor a 2 out of the absolute value to make the coefficient of x equal to 1
![y=\sqrt{2}\sqrt{x-3}+3](https://tex.z-dn.net/?f=y%3D%5Csqrt%7B2%7D%5Csqrt%7Bx-3%7D%2B3)
find a, h and k for ![y=\sqrt{2}\sqrt{x-3}+3](https://tex.z-dn.net/?f=y%3D%5Csqrt%7B2%7D%5Csqrt%7Bx-3%7D%2B3)
![a=1.41421356\\ h=3\\k=3](https://tex.z-dn.net/?f=a%3D1.41421356%5C%5C%20h%3D3%5C%5Ck%3D3)
the horizontal shift depends on the value of h when
, the horizontal shift is described as:
- the graph is shifted to the left h units
- the graph is shifted to the right h units
the vertical shift depends on the value of k