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:

Option (A)

Step-by-step 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,

$4=a(b)^{(-2)}$

$4=\frac{a}{b^{2} }$ ------(1)

For second point (-1, 2),

$2=a(b)^{-1}$

$2=\frac{a}{b}$ -----(2)

Dividing equation (1) by equation (2),

$\frac{4}{2}=\frac{\frac{a}{b^2}}{\frac{a}{b} }$

$2=\frac{a}{b^{2}}\times \frac{b}{a}$

$2=\frac{1}{b}$

b = $\frac{1}{2}$

From equation (1),

$4=\frac{a}{(\frac{1}{2} )^2}$

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) = $1.(\frac{1}{2})^{x}$

$f(x)=(\frac{1}{2})^x$

Option (A) will be the answer.