The third graph or bottom left graph represents [tex]f(x) = 0.2^{x} + 3.[/tex]
Step-by-step explanation:
Step 1:
To determine which of the given graphs represents the equation [tex]f(x) = 0.2^{x} + 3[/tex], we substitute some values in the place of x.
When [tex]x=0,[/tex] [tex]f(x) = 0.2^{x} + 3, f(0) = 0.2^{0} + 3= 4.[/tex]
Anything with an exponent of 0 will equal 1.
So the graphs on the right side cannot be the answers.
Step 2:
Now we substitute another value to determine which graph represents [tex]f(x) = 0.2^{x} + 3.[/tex]
When [tex]x=1,[/tex] [tex]f(x) = 0.2^{x} + 3, f(1) = 0.2^{1} + 3= 4.2.[/tex]
The value of f(x) when [tex]x=1[/tex] is lesser than the value of f(x) when [tex]x =0.[/tex]
So the third graph or bottom left graph represents [tex]f(x) = 0.2^{x} + 3.[/tex]
