Answer to Question #278436 in Calculus for lemuel

Question

Can You Show Me the Way? Complete the table of values of the exponential function. Then, draw its graph in the given coordinate plane. 2 3 1 х -3 -2 -1 0 f(x) = 3*1. How will you describe the graph? 2. In which quadrant/s do the graph occupies?3. What are the other possible values of x? Describe the range of the possible values of x? 4.What do you think now is the range of the function? 5. What other observations can you give?

Answer 1

1.

$f(x)=3^x$

x f(x)

-3 1/27

-2 1/9

-1 1/3

0 1

1 3

2 9

3 27

domain: $x\isin (-\infin,\infin)$

y-intercept: $(0,1)$

no x-intercepts

f(x) is increasing in all domain

2.

f(x) is in first and second quadrants

3.

possible values of x:

$x\isin (-\infin,\infin)$

4.

range: $y\isin (0,\infin)$

5.

horizontal asymptote:

$y=0$

$f(x)<1$ for $x<0$

$f(x)>1$ for $x>0$