Question

Given four functions, place them in order of their y-intercept, from highest to lowest. f(x) g(x) h(x) j(x) the function f of x equals 4 to the x minus 2 power, plus 2 g(x) = 3(20)x Al is monitoring the decay of a population of fungi. It is reducing in half every four weeks. The population started at 14. x j(x) 1 5.00 2 2.50 3 1.25

Answer 1

Answer:

The order of the function according to the y-intercept is  $h(x)>j(x)>g(x)>f(x)$.

Step-by-step explanation:

The given function f(x) is,

$f(x)=4^{x-2}+2$

Put x=0,

$f(0)=4^{0-2}+2=2.0625$

The y intercept of f(x) is 2.0625.

The given function g(x) is,

$g(x)=3(20)^x$

Put x=0,

$g(x)=3(20)^0=3$

The y intercept of g(x) is 3.

The h(x) is monitoring the decay of a population of fungi. It is reducing in half every four weeks. The population started at 14.

Since the initial population is 14 therefore the y intercept of h(x) is 14.

The value of y in g(x) are in geometric progression with half as common ratio or the function j(x) can be defined as,

$j(x)=10(\frac{1}{2} )^x$

Put x=0,

$j(0)=10(\frac{1}{2} )^0=10$

The y intercept of j(x) is 10.

Therefore the order of function according to the y-intercept is,

$h(x)>j(x)>g(x)>f(x)$

Answer 2

The y-intercept is the value of the function when x = 0.

1) f(x) = 4 ^ (x - 2) + 2

=> x = 0 => f(0) = 4 ^ (0 - 2) + 2 = = 4^(-2) + 2 = 1/16 + 2 = 2.0625


2) g(x) = 3(20)^x  => x = 0 => 3 (20)^ 0 = 3(1) = 3

3) h(x)

Al is monitoring the decay of a population of fungi. It is reducing in half every four weeks. The population started at 14.

the y-intercept is the population at x = 0 which is 4

4)    x     j(x)
       1      5.0
       0      2 <--------- this is the y intercept
       2.5   0
       3      1.25

So, the order is 14 > 3 > 2.0625 > 2

=> h(x) > g(x) > f(x) > j(x) <-------- answer