Question

What is the y-intercept of an exponential function with no stated "a" value?

Answer 1

Given :

Exponential function

To find :

y intercept

Solution :

Exponential function :

A function which has the form as

$y = f(x) = a \times ( {b}^{x} )$

where

$a \neq0 \\ b > 0 \\ and \\ x \in \: real \: number$

Basically exponential function has similar shape in all graphs as shown in figure.

Exponential function is asymptotic to the x axis, so it has no intercept at x axis.

Because

a and b can not be 0 in this function.

• If b >1 (increasing function) , the left side of graph aproach to the y value of 0 and right side aproach to the positive infinity.
• If 0<b<1 (decreasing function), the right side of graph aproach to the y value of 0 and left side aproach to the positive infinity.

Exponential function always have y intercept,

at x= 0

y = ab° = a

which cut y axis at a when the value of x is equal to 0.

The value of a can be positive or negative but not 0.

As

$y = f(0) = ab ^{0} = a \times 1 = a$

So The y intercept of exponential function = a.