Question

Y=3(2)^x what is the y intercept the x intercept and is the graph increasing or decreasing

Answer 1

This is an exponential function, with base 2. Since 2 is greater than 1, the function is increasing.

For the y intercept, we have to set $x=0$, and we have

$y=3\cdot 2^0=3\cdot 1=3$

For the x intercept, we have to set $y=0$ and solve for x:

$3\cdot 2^x=0\iff 2^x=0$

And this has no solution. All we can say is that

$\displaystyle \lim_{x\to-\infty}2^x=0$

So, the x axis is an asymptote for the function, but the graph neves crosses it.

Answer 2

Answer:

y-intercept: (0, 3)

x-intercept: There isn't one

The graph is increasing.

Step-by-step explanation:

To find the y-intercept of a function, simply substitute 0 in for x, and calculate.

To find the x-intercept of a function, simply substitute 0 in for y, and solve for x.

To know whether the graph is increasing or decreasing, you need to look at what happens to the y-values as the value of x increases. If the values get bigger, it's increasing and if they get smaller it's decreasing.