Question

Which of the following exponential functions is represented by the graph? Question 15 options: A) ƒ(x) = (1∕2)x B) ƒ(x) = 2x C) ƒ(x) = −2x D) ƒ(x) = (1∕2)−x

Answer 1

Answer:Answer:

Option (A)

Explanation:

Let the equation of the exponential function is f(x) = a(b)ˣ

Two points (-2, 4) and (-1, 2) lie on the graph,

For (-2, 4),

By substituting the values in the given function,

------(1)

For second point (-1, 2),

-----(2)

Dividing equation (1) by equation (2),

b =

From equation (1),

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) =

Option (A) will be the answer.

Explanation:

Answer 2

Option (A)

Explanation:

Let the equation of the exponential function is f(x) = a(b)ˣ

Two points (-2, 4) and (-1, 2) lie on the graph,

For (-2, 4),

By substituting the values in the given function,

`4=a(b)^((-2))`

`4=(a)/(b^(2) )` ------(1)

For second point (-1, 2),

`2=a(b)^(-1)`

`2=(a)/(b)` -----(2)

Dividing equation (1) by equation (2),

`(4)/(2)=((a)/(b^2))/((a)/(b) )`

`2=(a)/(b^(2))* (b)/(a)`

`2=(1)/(b)`

b =
`(1)/(2)`

From equation (1),

`4=(a)/(((1)/(2) )^2)`

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) =
`1.((1)/(2))^(x)`

`f(x)=((1)/(2))^x`

Option (A) will be the answer.