I need help on my homework, please help!!

The graph of the function y=(1/2)^x is shown at right.

a. Describe what happens to y as x gets larger and larger. For example, what is y when x=20? x=100? x=1000? x=n(a much larger number)?

b. Does the graph of y=(1/2)^x have an x‑intercept? Explain how you know.

c. Does y=(1/2)^x have a vertical asymptote? In other words, is there a vertical line that the graph above approaches? Why or why not?

a) y approaches zero

b) The graph has no x-intercept

c) The graph does not have vertical asymptote.

Step-by-step explanation:

The given function is

When x=20,

when x=100,

When x=1000,

As x is getting larger, y is approaching zero.

b) The graph of

does not have x-intercepts.

Because when y=0, we get:

This gives us:

Which is false.

Meaning the graph has no x-intercept , it is asymptotic to the x-axis.

c) The graph does not have a vertical asymptote.

For a vertical asymptote, the denominator of the function is zero.

So

But we know that an exponential function is never zero.

Therefore the graph has no vertical asymptote

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.