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Sagot :
To determine the value of \( x \) at which the graph of the function \( F(x) = \frac{5x}{2x-6} \) has a vertical asymptote, we need to find the value of \( x \) that makes the denominator equal to zero, since division by zero is undefined and causes a vertical asymptote.
Let's analyze the denominator \( 2x - 6 \):
1. Set the denominator equal to zero:
[tex]\[ 2x - 6 = 0 \][/tex]
2. Solve for \( x \):
[tex]\[ 2x - 6 = 0 \][/tex]
Add 6 to both sides:
[tex]\[ 2x = 6 \][/tex]
Divide both sides by 2:
[tex]\[ x = 3 \][/tex]
Thus, the function \( F(x) = \frac{5x}{2x-6} \) has a vertical asymptote at \( x = 3 \). This occurs because at \( x = 3 \), the denominator becomes zero, leading to an undefined value for \( F(x) \).
Therefore, the correct answer is:
A. 3
Let's analyze the denominator \( 2x - 6 \):
1. Set the denominator equal to zero:
[tex]\[ 2x - 6 = 0 \][/tex]
2. Solve for \( x \):
[tex]\[ 2x - 6 = 0 \][/tex]
Add 6 to both sides:
[tex]\[ 2x = 6 \][/tex]
Divide both sides by 2:
[tex]\[ x = 3 \][/tex]
Thus, the function \( F(x) = \frac{5x}{2x-6} \) has a vertical asymptote at \( x = 3 \). This occurs because at \( x = 3 \), the denominator becomes zero, leading to an undefined value for \( F(x) \).
Therefore, the correct answer is:
A. 3
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