Question

1. identify the ( x- ) and ( y- ) intercepts of the graph of ( f(x) = \frac{x - 9}{x + 3} ) and explain how they are found.

Explanation:

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

Set $f(x) = 0$, so $\frac{x-9}{x+3} = 0$. A rational function equals 0 when its numerator is 0 (denominator ≠ 0).
$x - 9 = 0$

Step2: Solve for x

$x = 9$
Verify denominator: $9 + 3 = 12 ≠ 0$, so valid.

Step3: Find y-intercept (set x=0)

Substitute $x = 0$ into $f(x)$:
$f(0) = \frac{0 - 9}{0 + 3}$

Step4: Simplify to find y

$f(0) = \frac{-9}{3} = -3$

Answer:

x-intercept: $(9, 0)$; found by setting $f(x)=0$ and solving for $x$ (since the numerator must be 0 for the rational function to equal 0, while the denominator is non-zero at $x=9$).
y-intercept: $(0, -3)$; found by substituting $x=0$ into the function and calculating the resulting $f(x)$ value.