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:

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

will be strictly increasing, and we will find:

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

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

 

[CellCoree]

I am not able to provide a specific graph for this function without knowing more information about the parent function and the specific translation that has taken place. However, I can provide some general guidance on how to approach this problem.

First, it is important to understand the given information about the domain, interval of increase, and range. The domain (x=R) means that the function is defined for all real numbers. The interval of increase (-∞, ∞) means that the function is increasing for all values of x. The range (f(x) = R | f(x) > -3) means that the function has a minimum value of -3, but can take on any other value greater than -3.

To find the parent function for this situation, you can start by considering some common parent functions such as linear, quadratic, exponential, or trigonometric functions. For example, if you choose the linear parent function f(x) = x, the translated function may look like f(x) = x - 3, which would fit the given range of f(x) > -3. However, it is important to keep in mind that there are many possible parent functions that could fit this situation, so it may be helpful to experiment with different options to see which one best fits the given information.

Once you have identified a potential parent function, you can then use your knowledge of translations to create a graph that fits the given information. For example, if the parent function is f(x) = x, a translation of -3 units in the y-direction would result in the translated function f(x) = x - 3. You can then plot points on the graph to visualize how the translated function would look. It may also be helpful to use a graphing calculator or software to create a more accurate graph.

In summary, the key to drawing a graph for this function is to first understand the given information about the parent function and the translation, and then use that information to create a graph that fits the given criteria. Keep in mind that there may be multiple possible graphs that could fit this situation, so it is important to choose a parent function and translation that best fits the given information.