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1. Let Find the values of \(f(x) = \frac{2x^2 - 50}{x^2 + 2x - 15}.\)find the value of X for which f(x) is not defined. Enter all such values, separated by commas

2.Let \(y = \frac{x - 3}{x + 7}.\)Then this equation can be expressed in the form (x+a)(y+b)=c for some constants a b and c Enter your answer in the form " a,b,c ".

3.Let \(f(x) = \frac{2x^2 - 50}{x^2 + 2x - 15}.\)Find the values of k for which the equation x=k is a vertical asymptote of the graph of y=f(x) Enter all such values, separated by commas.

4. Enter the equation of the horizontal asymptote of the graph of \(f(x) = \frac{7x^3 - x^2 - 2}{3x^5 + 14x^2 + 33x + 8}.\)

 Apr 15, 2024
 #1
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Problem 1:

The function simplifies to f(x) = 2(x + 5)/(x + 3).  You can then see that the function is not defined for x = -3.

 Apr 15, 2024
 #2
avatar+179 
0

Problem 2:

 

We can rewrite the equation in the desired form by multiplying both sides by the denominator of the original equation, (x+7).

 

Steps to solve:

 

Multiply both sides by (x+7): y * (x + 7) = (x - 3)

 

Substitute y with its definition: (x - 3)/(x + 7) * (x + 7) = (x - 3)

 

Simplify: x - 3 = (x - 3)

 

Now, we can see that the equation holds true for any value of x (as long as x ≠ -7 to avoid dividing by zero in the original equation). This means we can set the right side to any constant value (c) to maintain the truth of the equation.

 

However, to achieve the desired form (x + a)(y + b) = c, we should choose c = 0 (since the right side is already 0).

 

Therefore, a = 0, b = -7 (as y is replaced by (x - 3)/(x + 7)), and c = 0.

'

The answer in the form a, b, c is: 0, -7, 0

 Apr 15, 2024

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