MHB A possible graph for this function?

[eleventhxhour]

I'm not sure how to draw the graph for this question. Could someone please point me in the right direction? I'm also not really sure how you'd find the parent function for the situation. Here's the question:

1) Each of the following situations involve a parent function whose graph has been translated. Draw a possible graph that fits the situation.
a) The doman is (x=R), the interval of increase is (-∞, ∞) and the range is (f(x) = R | f(x) > -3).

Thanks!

 

[MarkFL]

What kind of function is bounded at the left end (as $x\to-\infty$) by some finite value, but is unbounded at the right end and always increases? Could it be a polynomial of some type? A trigonometric, logarithmic or exponential function?

 

[eleventhxhour]

What kind of function is bounded at the left end (as $x\to-\infty$) by some finite value, but is unbounded at the right end and always increases? Could it be a polynomial of some type? A trigonometric, logarithmic or exponential function?

Um I'm not sure. An exponential function?

 

[MarkFL]

Um I'm not sure. An exponential function?

Yes, an exponential function of the form:

$$f(x)=ab^x+c$$ where $$a\ne0$$ and $$1<b$$

will be strictly increasing, and we will find:

$$\lim_{x\to-\infty}f(x)=c$$

So, can you pick appropriate values for $a,b,c$ such that the requirements of the problem are satisfied?