Help please I need it done :(

Question

Suppose you are given the equation of an exponential function y=a(b)* , where a > 0, b > 0, b ≠ 1 .

 

a. explain how you would know whether the function was increasing or decreasing without looking at the graph.

 

b. How would you know the value of the y intercept without actually looking at the graph?

 

c. Suppose you didn't know the value of the y interceot. show and/or explain how you could calculate the value of the y intercept.

Answer 1

a)

An exponential function equation y = ab^x , where a > 0, b > 0, b ≠ 1

Here x is a variable.

a,b are constants.

Condition for increasing of exponential function is

b > 1.

Condition for decreasing of exponential function is

0 < b < 1.

Answer 2

c)

y intercept means the point at which y = ab^x  is touches the y-axis.

So the y intercept point is (0 , y)

Substitute point (0 , y) in equation y = ab^x ,Then we will get y intercept.

y = ab⁰   ⇒  y = a(1)  ⇒  y = a.

The y intercept is y = a.

Answer 3

b)

An exponential function y = ab^x

'a' is the value of the y intercept.