Question

graph the function. y=4(1/5)^x

Answer 1

\(\large\color{slate}{ y=4(1/5)^x }\) .

Are you allowed to use a graphic calculator, or you need to explain the graph (sort of) ?

Answer 2

graphing calculator is allowed... all i need is the graph and how u got it

Answer 3

Use this: https://www.desmos.com/calculator/

Answer 4

i have, i have the graph but i dont have a way of showing how to get it... in otherwords... we can use the calculator if it helps us to show how to graph it. ya know?

Answer 5

So you still need to explain what the graph looks like and why?

Answer 6

yes

Answer 7

will start from this: our graph is: \(\large\color{slate}{ y=4(1/5)^{x} }\)

when x is a big negative number:
~~~~~~~~~~~~~~~~~~~~~~~
\(\large\color{slate}{ y=4(1/5)^{-10} }\)

\(\large\color{teal}{ y=4(5)^{10} }\)
~~~~~~~~~~~~~~~~~~~~~~~~
\(\large\color{slate}{ y=4(1/5)^{-100} }\)

\(\large\color{teal}{ y=4(5)^{100} }\)
~~~~~~~~~~~~~~~~~~~~~~~~
\(\large\color{slate}{ y=4(1/5)^{-1000} }\)

\(\large\color{teal}{ y=4(5)^{1000} }\)
~~~~~~~~~~~~~~~~~~~~~~~~

Answer 8

see what I am doing?

Answer 9

actualy... yes

Answer 10

very good, so when x goes more and more into \(\normalsize\color{slate}{ \rm -\infty }\), the y goes where?

Answer 11

opposit of the x????

Answer 12

yes.

Answer 13

the y becomes a very very big positive number.

Answer 14

now, lets find the y-intercept of the function.
Can you do this?

Answer 15

given the rule that: \(\normalsize\color{royalblue}{ (b)^0=1 }\), for any real number \(\normalsize\color{royalblue}{ b }\),
with an exception that \(\normalsize\color{royalblue}{ b\ne0 }\)

Answer 16

i got this.... i think i am off to a good start thanks... how can medals be given???? i will give if u tell me how

Answer 17

my connection is playing games

Answer 18

\(\normalsize\color{royalblue}{ y=4(1/5)^x }\)
plug in \(\normalsize\color{royalblue}{ 0 }\) instead of \(\normalsize\color{royalblue}{ x }\).

\(\normalsize\color{royalblue}{ y=4(1/5)^0 }\). And \(\normalsize\color{royalblue}{ y=? }\)

Answer 19

aha! figured it out... gave u medal thank u so much!.. the graph looks like a take off from left to right starting out beneath the x axis...

Answer 20

but the graph will never have a y value that is zero or less.

Answer 21

okay, as the graph \(\normalsize\color{royalblue}{ y=4(1/5)^{x} }\) has bigger x values, the smaller \(\normalsize\color{royalblue}{ 1/5 }\) will get, and that means you are multiplying 4 times a smaller number.

Answer 22

when \(\normalsize\color{royalblue}{ x=1}\)
\(\normalsize\color{royalblue}{ y=4(1/5)^{1} =4/5 }\)
~~~~~~~~~~~~~~~~~
when \(\normalsize\color{royalblue}{ x=2}\)
\(\normalsize\color{royalblue}{ y=4(1/5)^{2} =4/25 }\)
~~~~~~~~~~~~~~~~~
when \(\normalsize\color{royalblue}{ x=3}\)
\(\normalsize\color{royalblue}{ y=4(1/5)^{3} =4/125 }\)
~~~~~~~~~~~~~~~~~
when \(\normalsize\color{royalblue}{ x=4}\)
\(\normalsize\color{royalblue}{ y=4(1/5)^{4} =4/625 }\)
~~~~~~~~~~~~~~~~~
when \(\normalsize\color{royalblue}{ x=5}\)
\(\normalsize\color{royalblue}{ y=4(1/5)^{5} =4/3125 }\)

Answer 23

so it will be hitting zero closer and closer, so it should look like