Which graph represents this equation-3x + 4y= -12
1 answer:
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The asymptotes of the graph of are as follows:
- Vertical: x = 1.
- Horizontal: y = 0.
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
In this problem, the function is:
For the vertical asymptote, we have that:
.
For the horizontal asymptote, we have that:
.
More can be learned about asymptotes at brainly.com/question/16948935
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Answer:
See below.
Step-by-step explanation:
So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.
Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.
Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.
Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:
In other words, we will have:
, where n is some value.
Let's determine n first. We know that f(0)=64, thus:
Now, let's expand:
Expand:
This is the simplest it can get.
