Given the function:
[tex]f(x)=\frac{2x^2}{x^2+4}[/tex]
when x=-2, f(x) = ?
Substitute the value of -2 for x in the f(x) function.
[tex]\begin{gathered} f(x)=\frac{2x^2}{x^2+4} \\ f(-2)=\frac{2(-2)^2}{(-2)^2+4}=1 \end{gathered}[/tex]
when x = -1, f(x) =?
Substitute the value of -1 for x in the f(x) function.
[tex]\begin{gathered} f(x)=\frac{2x^2}{x^2+4} \\ f(-1)=\frac{2(-1)^2}{(-1)^2+4}=\frac{2}{5} \end{gathered}[/tex]
when x = 5, f(x) =?
Substitute the value of 5 for x in the f(x) function.
[tex]\begin{gathered} f(x)=\frac{2x^2}{x^2+4} \\ f(5)=\frac{2(5)^2}{(5)^2+4}=\frac{50}{29} \end{gathered}[/tex]
when x = 6, f(x) =?
Substitute the value of 6 for x in the f(x) function.
[tex]\begin{gathered} f(x)=\frac{2x^2}{x^2+4} \\ f(6)=\frac{2(6)^2}{(6)^2+4}=\frac{9}{5} \end{gathered}[/tex]
Thus, we have
[tex]\begin{gathered} x=-2,\text{ f(}x)\text{ =}1 \\ x=-1,\text{ f(x)=}\frac{2}{5} \\ x=5,\text{ f(x)=}\frac{50}{29} \\ x=6,\text{ f(x)=}\frac{9}{5} \end{gathered}[/tex]
The graph of the f(x) function is as shown below:
