college algebra: f(x)=5^x is shifted 8 right, 3 down; new function is...?

[hoosierok]

Write an equation of the following graph in its final position.

The graph of yequals=5 Superscript x5x
is translated 88
units to the rightright
and 33
units downwarddownward.



The transformed equation is nothing.

​(Simplify your​ answer.)

 

[Deleted member 4993]

Write an equation of the following graph in its final position.

The graph of yequals=5 Superscript x5x
is translated 88
units to the rightright
and 33
units downwarddownward.



The transformed equation is nothing.

​(Simplify your​ answer.)

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

Write an equation of the following graph in its final position.

The graph of yequals=5 Superscript x5x
is translated 88
units to the rightright
and 33
units downwarddownward.

Did you not notice that much of the above is repeated and unclear...? :shock:

I suspect that the exercise is meant to read as follows:

---

The graph of y = 5^x is translated eight units to the right and three units downward. Write the equation of the graph in its final position.

---

Is this correct? If not, please reply with corrections. If so, please reply with a clear listing of your efforts so far, showing where you are getting stuck in the function transformation. (here) Thank you!

 

[hoosie]

Transformation of Exponential Function

Example:
Shift graph of y = 2^{x
3units left and one unit up. Find the rule for the new graph. Draw both graphs on the one set of axes.}

<sup>G

Graph on right y = 2^x (base graph)
New graph on left y = 2^(x + 3) + 1

Note:
+ 3 means shift base graph 3 units left (opposite to + direction)
+ 1 means shift base graph 1 unit up (same as + direction)</sup>

 

[RalphD]

Example:
Shift graph of y = 2<sup>x
3units left and one unit up. Find the rule for the new graph. Draw both graphs on the one set of axes.

G

Graph on right y = 2^x (base graph)
New graph on left y = 2^(x + 3) + 1

Note:
+ 3 means shift base graph 3 units left (opposite to + direction)
+ 1 means shift base graph 1 unit up (same as + direction)</sup>

As Subhotosh Khan pointed out, you should share your work with us, even if you know it doesn't produce the right results. Copy-pasting an example is hardly that. Any line of reasoning would be a start. I for example might say "I know how to graph \(\displaystyle 2^x\) but I have no idea how to shift it", or perhaps "I know how to algebraically express a shift of an exponential function, but I don't know how to graph it". Something that tells us what you've tried and where you're stuck.

Giving a complete solution on how to graph some equation would be counterproductive as there are myriads of articles found via Google and sections found in books available that already do that.