Question

What is the y-intercept of exponential function?

Answer 1

Hint: By y-intercept we mean that we want to know where graph of the given function is intersecting with the y-axis and since it is on the y-axis therefore the value of x coordinate of the given function must be zero.

Complete step-by-step answer:
A function which has the form as $y=f(x)=a\times {{b}^{x}}$ where a is not equal to zero and b is greater than zero and x is a real number.
We know that exponential function is asymptotic to the x-axis because of which it has no intercept with the x-axis.
a and b can not be zero in this function
- If we have increasing function or we can say b>1, the left side of the graph approaches the y-value of 0 and we see from the graph that the right side approaches the positive infinity.
- If 0We must know that exponential function always has y-intercept,
At x=0
$y=a{{b}^{0}}=a$
And it cuts y-axis when x=0
And the value of a can be greater or less than zero but not equal to zero.
As $y=f(0)=a{{b}^{0}}=a\times 1=a$
So, we can say that the y-intercept of the exponential function is a.

Note: We must try to give answers to such questions after observing the graph and even try to give answers in values using graphical methods if possible. Power and exponent is not asked very deeply so be confident while answering.