(a)

The statement is " is an exponential function of ".

The above statement is false.

Because an exponential function is never zero.

Observe the given table of values :

The value of , when .

So, connot be an exponential function of .

(b)

The statement is " is a logarithmic function of ".

The above statement is true.

Consider the logarithmic function as .

Substitute and in the above function.

Since cannot be zero, the value of .

Substitute and in .

Substitute in above equation.

.

Substitute the values and in .

Thus, the logarithmic function is .

Check whether the function satisfies the third point or not.

Substitute and in .

Since the above statement is true, is a logarithmic function of .

(c)

The statement is " is an exponential function of ".

The above statement is true.

From part (b), conclude that is a logarithmic function of .

Thus, the logarithmic function is .

Definition of logarithmic function :

.

It is an exponential function of .

(d)

The statement is " is a linear function of ".

The above statement is false.

Slope of the line joining and : .

Slope of the line joining and : .

Since slope of the line joining and is not equals to slope of the line joining and ,

cannot be an linear function of ".

(a) False.

(b) True.

(c) True.

(d) False.