which function has the greatest x - intercept?\n$f(x)=3x - 9$\n$g(x)=|x + 3|$\n$h(x)=2^{x}-16$\n$j(x)=-5(x…

Explanation:

Step1: Find (x) - intercept of (f(x)=3x - 9)

Set (f(x)=0), then (3x-9 = 0). Add (9) to both sides: (3x=9). Divide by (3): (x = 3).

Step2: Find (x) - intercept of (g(x)=\vert x + 3\vert)

Set (g(x)=0), then (\vert x+3\vert=0). By the property of absolute value (x + 3=0), so (x=-3).

Step3: Find (x) - intercept of (h(x)=2^{x}-16)

Set (h(x)=0), then (2^{x}-16 = 0). Rewrite (16) as (2^{4}), so (2^{x}=2^{4}). By the property of exponential functions (x = 4).

Step4: Find (x) - intercept of (j(x)=-5(x - 2)^{2})

Set (j(x)=0), then (-5(x - 2)^{2}=0). Divide by (-5): ((x - 2)^{2}=0). Take square root: (x-2=0), so (x = 2).

Answer:

(h(x)=2^{x}-16)