Answer:
The order of the function according to the y-intercept is [tex]h(x)>j(x)>g(x)>f(x)[/tex].
Step-by-step explanation:
The given function f(x) is,
[tex]f(x)=4^{x-2}+2[/tex]
Put x=0,
[tex]f(0)=4^{0-2}+2=2.0625[/tex]
The y intercept of f(x) is 2.0625.
The given function g(x) is,
[tex]g(x)=3(20)^x[/tex]
Put x=0,
[tex]g(x)=3(20)^0=3[/tex]
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,
[tex]j(x)=10(\frac{1}{2} )^x[/tex]
Put x=0,
[tex]j(0)=10(\frac{1}{2} )^0=10[/tex]
The y intercept of j(x) is 10.
Therefore the order of function according to the y-intercept is,
[tex]h(x)>j(x)>g(x)>f(x)[/tex]
A function assigns the values. The four functions are placed in order of their y-intercept, from highest to lowest as, h(x)>j(x)>g(x)>f(x).
A function assigns the value of each element of one set to the other specific element of another set.
For the given four functions, the value of the y-intercept can be written as,
A.)
f(x) = 4ˣ⁻² + 2
To find the y-intercept substitute the value of x as 0 in the given function,
f(0) = 4⁰⁻² + 2 = 33/16 = 2.0625
B.)
g(x) = 3(20)ˣ
To find the y-intercept substitute the value of x as 0 in the given function,
g(0) = 3(20)⁰ = 3
C.)
In the given case, The h(x) is monitoring the decay of a population of fungi. It is reduced by half every four weeks. The population started at 14. therefore, the y-intercept of the given function will be 14.
D.)
j(x) = 10(1/2)ˣ
To find the y-intercept substitute the value of x as 0 in the given function,
j(0) = 10(1/2)⁰ = 10
Hence, the four functions are placed in order of their y-intercept, from highest to lowest as, h(x)>j(x)>g(x)>f(x).
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