Answer:
[tex]f(x) = 3( {2}^{x})[/tex]
Step-by-step explanation:
Considering all the options, second option:
[tex]f(x) = 3( {2}^{x})[/tex]
At y-intercept, when x = 0
y = f(0) = 3(2⁰)
y = 3 × 1
y = 3
The coordinate of y-intercept is (0,3) which corresponds to the y-intercept point given in the graph.
While other options will not give y = 3 when x = 0.
At x - intercept, when y = 0
[tex]0 = 3( {2}^{x})[/tex]
Divide both sides by 3
[tex] {3}^{x} = 0[/tex]
No value of x that 3 will raise to, to give 0 therefore x is undefined i.e the graph tends to infinity. All other options satisfy this condition too.
Also when x = 1,
f(1) = 3(2^(1))
f(1) = 3 × 2
f(1) = 6
This substitution nullifies the option 3(3^x) because when x = 1, its f(1) = 3(3) = 9 not 6.
Hence, second option
[tex]f(x) = 3( {2}^{x})[/tex]
is the exponential function that is represented by the graph.