Question

consider the function.
g(x)=√(x + 4) - 6
which function has the same y - intercept as this
function?
○ f(x)=4/(x - 8) - 3.5
○ f(x)= - 4/x - 1
○ f(x)=2|x + 2|
○ f(x)=|x - 4|

Explanation:

Step1: Find y-intercept of $g(x)$

Set $x=0$: $g(0)=\sqrt{0+4}-6 = \sqrt{4}-6 = 2-6 = -4$

Step2: Check y-intercept of first option

Set $x=0$: $f(0)=\frac{4}{0-8}-3.5 = -0.5-3.5 = -4$

Step3: Verify other options (optional)

Option2: $f(0)=-\frac{4}{0}-1$ (undefined)
Option3: $f(0)=2|0+2|=4$
Option4: $f(0)=|0-4|=4$

Answer:

$\boldsymbol{f(x)=\frac{4}{x-8}-3.5}$