<h3>
Answer: No, this isn't a function.</h3>
Why not? Focus on the two points (0,2) and (0,4)
We have the x value x = 0 show up twice. Any time x repeats itself like this, it leads to "not a function" as the result.
In other words, the input x = 0 leads to multiple outputs y = 2 and y = 4 at the same time. A function is only possible if every x input leads to exactly one y output.
If you are a visual learner, then plot all of the points on the same xy grid. Then notice how (0,2) and (0,4) fail the vertical line test to show we don't have a function.
Side note: The y values can repeat themselves in a function.
The same as last time
Step-by-step explanation:
![\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}](https://tex.z-dn.net/?f=%5Cboxed%7B%28r-s%29%28x%29%3D-3x-1%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28r%5Ccdot%20s%29%28x%29%3D10x%5E2-5x%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28r%2Bs%29%28-2%29%3D-15%7D)
<h2>
Explanation:</h2>
In this exercise, we have the following functions:
![r(x)=2x-1 \\ \\ s(x)=5x](https://tex.z-dn.net/?f=r%28x%29%3D2x-1%20%5C%5C%20%5C%5C%20s%28x%29%3D5x)
And they are defined for all real numbers x. So we have to write the following expressions:
First expression:
![(r-s)(x)](https://tex.z-dn.net/?f=%28r-s%29%28x%29)
That is, we subtract s(x) from r(x):
![(r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}](https://tex.z-dn.net/?f=%28r-s%29%28x%29%3D2x-1-5x%20%5C%5C%20%5C%5C%20Combine%20%5C%20like%20%5C%20terms%3A%20%5C%5C%20%5C%5C%20%28r-s%29%28x%29%3D%282x-5x%29-1%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28r-s%29%28x%29%3D-3x-1%7D)
Second expression:
![(r\cdot s)(x)](https://tex.z-dn.net/?f=%28r%5Ccdot%20s%29%28x%29)
That is, we get the product of s(x) and r(x):
![(r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}](https://tex.z-dn.net/?f=%28r%5Ccdot%20s%29%28x%29%3D%282x-1%29%285x%29%20%5C%5C%20%5C%5C%20By%20%5C%20distributive%20%5C%20property%3A%20%5C%5C%20%5C%5C%20%28r%5Ccdot%20s%29%28x%29%3D%282x%29%285x%29-%281%29%285x%29%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28r%5Ccdot%20s%29%28x%29%3D10x%5E2-5x%7D)
Third expression:
Here we need to evaluate:
![(r+s)(-2)](https://tex.z-dn.net/?f=%28r%2Bs%29%28-2%29)
First of all, we find the sum of functions r(x) and s(x):
![(r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1](https://tex.z-dn.net/?f=%28r%2Bs%29%28x%29%3D2x-1%2B5x%20%5C%5C%20%5C%5C%20Combine%20%5C%20like%20%5C%20terms%3A%20%5C%5C%20%5C%5C%20%28r%2Bs%29%28x%29%3D%282x%2B5x%29-1%20%5C%5C%20%5C%5C%20%28r%2Bs%29%28x%29%3D7x-1)
Finally, substituting x = -2:
![(r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}](https://tex.z-dn.net/?f=%28r%2Bs%29%28-2%29%3D7%28-2%29-1%20%5C%5C%20%5C%5C%20%28r%2Bs%29%28-2%29%3D-14-1%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28r%2Bs%29%28-2%29%3D-15%7D)
<h2>Learn more: </h2>
Parabola: brainly.com/question/12178203
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