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For what value of [tex][tex]$x$[/tex][/tex] does the graph of the following function [tex][tex]$f(x)$[/tex][/tex] have a vertical asymptote?

[tex][tex]$f(x) = \frac{3}{x+5}$[/tex][/tex]

A. 5
B. 3
C. -5
D. 3

Sagot :

GinnyAnsweridn
To find the value of [tex]\( x \)[/tex] where the function [tex]\( F(x) = \frac{3}{x+5} \)[/tex] has a vertical asymptote, we need to determine the value of [tex]\( x \)[/tex] that makes the denominator zero, as a vertical asymptote occurs where the function value tends to infinity, which happens when the denominator is zero in a rational function.

Let's set the denominator equal to zero:
[tex]\[ x + 5 = 0 \][/tex]

Next, we solve for [tex]\( x \)[/tex]:
[tex]\[ x = -5 \][/tex]

Thus, the value of [tex]\( x \)[/tex] where the function [tex]\( F(x) \)[/tex] has a vertical asymptote is [tex]\( -5 \)[/tex].

So, the correct answer is:
C. [tex]\(-5\)[/tex]
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