Answer:
The two functions intersect, and the value of [tex]f(0)[/tex] is greater than the value of [tex]g(0)[/tex].
Step-by-step explanation:
Given:
The function [tex]f(x) =3x+6[/tex]
The function [tex]g(x)[/tex] has slope 6 and y-intercept 3.
A linear function is of the form: [tex]y=mx+b[/tex], where, 'm' is the slope and 'b' is the y-intercept.
Therefore, the equation of the function [tex]g(x)[/tex] with 'm' equal to 6 and 'b' equal to 3 is given as:
Also, the slope of function [tex]g(x)[/tex] is 3 and y-intercept is 6.
Now, option 1 is incorrect as their slopes are different.
Two lines of different slopes can't represent same line. So, option 2 is also incorrect.
[tex]g(x)=6x+3[/tex]
The value of [tex]f(0) =3\times0+6=6[/tex]
The value of [tex]g(0)=6\times0+3=3[/tex]
Therefore, as 6 > 3, [tex]f(0)>g(0)[/tex]
Hence, the last option is correct.
