Question

epts of the following function. write your o select the appropriate number of x-inte\\(f(x) = \frac{3x + 27}{x + 2}\\)

Explanation:

Step1: Find x-intercept (set f(x)=0)

To find the x - intercept, we set \( f(x) = 0 \). So we have the equation \( \frac{3x + 27}{x + 2}=0 \). A fraction equals zero when the numerator is zero (and the denominator is not zero). So we solve \( 3x+27 = 0 \). Subtract 27 from both sides: \( 3x=-27 \). Divide both sides by 3: \( x=-9 \). Now we check the denominator at \( x = - 9 \): \( -9 + 2=-7
eq0 \), so \( x=-9 \) is valid.

Step2: Find y-intercept (set x = 0)

To find the y - intercept, we set \( x = 0 \) in the function \( f(x)=\frac{3x + 27}{x + 2} \). Substitute \( x = 0 \): \( f(0)=\frac{3(0)+27}{0 + 2}=\frac{27}{2}=13.5 \).

Answer:

x - intercept: \( x=-9 \) (or the point \((-9,0)\)), y - intercept: \( y = \frac{27}{2}\) (or the point \((0,\frac{27}{2})\))