Algebra Week 2 Equestion Functions Exercise Problems Help

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Ebfrl3693

Mathematics

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1) For the previous problem you worked on (Please see attachment) please spell out the answer to the question: Does the equation represent y as a function of x? (Note that your post does not include the word "function" at all.)

Please reply to specifically address the question. (This feedback is from my professor) Thank you!


2)

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Sol: 𝑥 3 𝑦 = −4 Dividing by x3 on both sides, we get 𝑥 3𝑦 4 = − 𝑥3 𝑥3 4 𝑦=− 3 𝑥 Hence. Also, from the above equation, we can see that y depends on the values of x except x = 0, So domain of the equation is 𝐷𝑜𝑚𝑎𝑖𝑛 = (−∞, 0) ∪ (0, ∞) And the range of the function is 𝑅𝑎𝑛𝑔𝑒 = (−∞, 0) ∪ (0, ∞)
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Explanation & Answer

It's okay. No problem.Here's the solution file.😊

Q1: - Does the equation represent y as a function of x?

Sol: First, we solve the equation for y.
𝑥 3 𝑦 = −4
Dividing by x3 on both sides, we get
𝑥3 𝑦
4
=

𝑥3
𝑥3
4
𝑦=− 3
𝑥
Now we check if the equation represents y as a function of x or not.
Keeping the definition of function in mind, which is:
“A function is a relation which assigns each input exactly one output. For y to
be a function of x, each x-value(input) must have exactly one corresponding yvalue(output)”
Using some values of x in the equation.
x

y
...


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