Question

expand the numerator and denominator of f(x) to complete the following information. k(x) = \frac{3(2x - 1)}{4(x - 3)} a. numerator: a. leading coefficient: b. degree: b. denominator: a. leading coefficient: b. degree: question 8 1 pts what is the horizontal asymptote of the function k(x) = \frac{3(2x - 1)}{4(x - 3)}? you can use the desmos graphing calculator to assist you if needed. \bigcirc y = \frac{3}{2}x \bigcirc y = \frac{3}{2} \bigcirc x = \frac{3}{2} \bigcirc y = x + \frac{3}{2}

Explanation:

Step1: Expand Numerator

Expand \( 3(2x - 1) \): \( 3\times2x - 3\times1 = 6x - 3 \).

Step2: Leading Coefficient (Numerator)

The leading term of \( 6x - 3 \) is \( 6x \), so leading coefficient is \( 6 \).

Step3: Degree (Numerator)

The highest power of \( x \) in \( 6x - 3 \) is \( 1 \), so degree is \( 1 \).

Step4: Expand Denominator

Expand \( 4(x - 3) \): \( 4\times x - 4\times3 = 4x - 12 \).

Step5: Leading Coefficient (Denominator)

The leading term of \( 4x - 12 \) is \( 4x \), so leading coefficient is \( 4 \).

Step6: Degree (Denominator)

The highest power of \( x \) in \( 4x - 12 \) is \( 1 \), so degree is \( 1 \).

Step7: Horizontal Asymptote

For a rational function \( \frac{N(x)}{D(x)} \) where degree of \( N(x) \) = degree of \( D(x) \), horizontal asymptote is \( y = \frac{\text{leading coefficient of } N(x)}{\text{leading coefficient of } D(x)} \). Here, \( \frac{6}{4} = \frac{3}{2} \), so horizontal asymptote is \( y = \frac{3}{2} \).

Answer:

s:
A. Numerator:
a. Leading Coefficient: \( 6 \)
b. Degree: \( 1 \)
B. Denominator:
a. Leading Coefficient: \( 4 \)
b. Degree: \( 1 \)
Question 8: \( y = \frac{3}{2} \) (Option: \( y = \frac{3}{2} \))