Homework Help

Can someone help me figure this question on functions and using transformations?Use...

user profile pic

deekoch | Student, Undergraduate | eNoter

Posted December 13, 2011 at 8:49 AM via web

dislike 0 like

Can someone help me figure this question on functions and using transformations?

Use transformations to graph the following function.  Also state a) the domain, b) the range, c) the horizontal asymptote.

5 Answers | Add Yours

Top Answer

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted December 16, 2011 at 11:09 AM (Answer #1)

dislike 1 like

Given `f(x)=2^(-x)-2` :

(a) The domain is all real numbers. Exponentials accept any x as input.

(b) The range is y>-2. The value of `2^(-x)` goes to zero as x tends to infinity, so the limit of the function is -2.

Thinking in terms of transformations, we translate the graph of `y=2^(-x)` down 2 units. Since `y=2^(-x)` has a horizontal asymptote of y=0, the new horizontal asymptote is y=-2.

(c) The horizontal asymptote is y=-2.

(d) The base graph is `y=2^x` . Changing the x to -x results in a reflection across the y-axis, and subtracting 2 is a vertical translation down 2 units.

`y=2^x` in black;`y=2^(-x)` in green;`y=2^(-x)-2` in red.

user profile pic

deekoch | Student, Undergraduate | eNoter

Posted December 13, 2011 at 8:51 AM (Answer #2)

dislike 0 like

oops, I forgot to give the function, that is f(x) =( 2^-2) - 2

user profile pic

rock-star790 | Student, Grade 10 | Salutatorian

Posted December 13, 2011 at 9:04 AM (Answer #3)

dislike 0 like

The question is a bit confusing, could you please rewrite the question?

user profile pic

rock-star790 | Student, Grade 10 | Salutatorian

Posted December 13, 2011 at 9:06 AM (Answer #4)

dislike 0 like

Is the question f(x)= (x^2-2) - 2?

 

user profile pic

deekoch | Student, Undergraduate | eNoter

Posted December 14, 2011 at 8:18 AM (Answer #5)

dislike 0 like

sowmyad96,

My question is: Use transformations to graph the following function and submit a graph.  Also state a) the domain, b) the range, c) the horizontal asymptote.  f(x) = (2^-x) - 2.  The -x is the exponent in the question.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes