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Find all vertical asymptotes of the following function.

f(x)=(2x+10)/(x^(2)-16)
Answer Attempt 1 out of 3
No Vertical Asymptotes

Question $\newline$ Watch Vi $\newline$ Find all vertical asymptotes of the following function. $\newline$ $f(x)=\frac{2 x+10}{x^{2}-16}$ $\newline$ Answer Attempt $1$ out of $3$ $\newline$ No Vertical Asymptotes

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Which word problem matches the one-step equation?

Full solution

Q. Question

\newline

Watch Vi

\newline

Find all vertical asymptotes of the following function.

\newline

f(x)=\frac{2 x+10}{x^{2}-16}

\newline

Answer Attempt

1

out of

3

\newline

No Vertical Asymptotes

Identify Vertical Asymptotes: To find the vertical asymptotes of the function, we need to determine where the denominator is equal to $0$ , because vertical asymptotes occur at values of $x$ that make the denominator undefined.
Set Denominator Equal to Zero: Set the denominator equal to zero and solve for $x$ : $x^2 - 16 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation: $(x - 4)(x + 4) = 0$ .
Find Values of x: Find the values of $x$ that make the equation true: $x - 4 = 0$ or $x + 4 = 0$ .
Solve Equations for $x$ : Solve each equation for $x$ : $x = 4$ and $x = -4$ .
Check Numerator for Zero: Check if these values of $x$ also make the numerator zero, because if they do, they might be holes instead of vertical asymptotes. The numerator is $2x + 10$ , so we plug in $x = 4$ and $x = -4$ to see if it equals zero.
Numerator for $x = 4$ : For $x = 4$ , the numerator is $2(4) + 10 = 8 + 10 = 18$ , which is not equal to zero.
Numerator for $x = -4$ : For $x = -4$ , the numerator is $2(-4) + 10 = -8 + 10 = 2$ , which is also not equal to zero.
Confirm Vertical Asymptotes: Since neither $x = 4$ nor $x = -4$ make the numerator zero, they are indeed vertical asymptotes of the function $f(x)$ .

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