How do I graph the function? State the y-intercept?

y=3(2^x)

Question

How do I graph the function? State the y-intercept?

y=3(2^x)

anonymous · Answer

For finding y intercept we put x = 0..

anonymous · Answer

The y-intercept occurs when x=0.  It is the point (0, y).  In this case, $$f(0)=3(2^0)=3$$So, your y-intercept is the point (0,3).

anonymous · Answer

Anything raised to the power 0 except 0 is 1.

So:

$$y = 3(2^0)  = 3(1) = 3$$

anonymous · Answer

Ok

anonymous · Answer

To graph this, it is best to recognize that your function is just a variant of the basic exponential function:$$f(x)=a^x$$|dw:1344222269360:dw|

anonymous · Answer

To make sense of this, first ask: how does the base "a", affect the graph?  Well, the basic shape of the curve is unchanged. In fact, if f(x)=a^x, the y-intercept is always (0,1) regardless of the value "a" takes.  But, the rate at which f(x) approaches zero and infinity greatly depend on the value "a" takes.

anonymous · Answer

I must add "the basic shape of the graph is unchanged" assumes a>0.