The function f(x) is defined as follows: f(x)= 3x+1 if x is less than or equal to 0 2x^2 if 0 4 if c is greater than or equal to 2determine the following values of the functionf(-3)= __ f(2)= ___

We have a function [tex]f(x)[/tex] defined by two rules: if [tex]x \leq 0[/tex], [tex]f(x)=3x+1[/tex], and if [tex]x \geq 2[/tex], [tex]f(x)=2 x^{2} [/tex]. Notice that when you are evaluating a function at a number, you are basically saying that [tex]x[/tex] is equal to that number. So, when you say [tex]f(-3)[/tex], you are saying that  [tex]x-3[/tex]. Since [tex]-3 \leq 0[/tex], we are going to use our first rule to evaluate our function at -3:
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]

Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]

We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].