Question

1) Answer the following questions for the function y= 4^x

Answer 1

a) Increasing function.

b) The growth factor is 4.

c) The asymptote is y tending to zero as x tends to negative infinity.

d) y = 1

c) The graph can be seen at the end.

What conclusions can we get about the given function?

Here we are given the following exponential function:

y =f(x) =  4^x

a) First, we want to know if the function is increasing or decreasing. Remember that a function is increasing if, as x increses, also does the value of y.

Here clearly we have an increasing function.

• f(0) = 4^0 = 1
• f(1) = 4^1 = 4
• f(2) = 4^2 = 16

and so on...

b) Now we want to identify the growth factor. This is the number that is being exponentiated, so in:

y = 4^x

The growth factor is 4.

c) We have an asymptote as x tends to negative infinity, because we will eventually have denominator that tends to infinity, then we will have an asymptote that tends to zero, as x tends to negative infinity.

d) The y-intercept is what we get when we evaluate in x = 0, we have:

y = f(0) = 4^0 = 1

The y-intercept is y = 1.

e) The sketch of the exponential function can be seen in the image below.

If you want to learn more about exponential functions:

brainly.com/question/11464095

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