Answer :

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.