Given:
The function is
[tex]f(x)=4x+9[/tex]
Domain = {-4, -2, 0, 2}
To find:
The range of the given function for the given domain.
Solution:
We know that domain is the set of input values and range is the set of output values.
We have, [tex]f(x)=4x+9[/tex] and domain = {-4, -2, 0, 2}.
Putting x=-4 in the given function, we get
[tex]f(-4)=4(-4)+9[/tex]
[tex]f(-4)=-16+9[/tex]
[tex]f(-4)=-7[/tex]
Putting x=-2 in the given function, we get
[tex]f(-2)=4(-2)+9[/tex]
[tex]f(-2)=-8+9[/tex]
[tex]f(-2)=1[/tex]
Putting x=0 in the given function, we get
[tex]f(0)=4(0)+9[/tex]
[tex]f(0)=0+9[/tex]
[tex]f(0)=9[/tex]
Putting x=2 in the given function, we get
[tex]f(2)=4(2)+9[/tex]
[tex]f(2)=8+9[/tex]
[tex]f(2)=17[/tex]
The output values are -7, 1, 9, 17. So, the range of the function f(x) for the given domain is {-7, 1, 9, 17}.
Therefore, the correct option is D.
