Couple of questions

E

Emisah

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Jan 28, 2006
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can anyone help me with these?


1. 14 Fully describe the following function. Be sure to describe its slope, y-intercept, and the intervals over which it is increasing, decreasing, or neither.
f(x)={ 3x+3 x>−1 0 otherwise

2. 6 Where do the following lines intersect (find by graphing)?
f(x)=−x+7 g(x)=3x+3

3. 4 The following is a graph of two functions: f(x)=2x [green], and a transformation of f(x). What is the function in blue?


4. 12 Find (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x).
f(x)=3x−2 g(x)= x 2

5. 12 Given the graph of f(x)=3x+2, find an expression for a graph of the same function shifted up two units, left two units, down two units, and right two units. Be specific about which function is for which transformation.
6. 12 Using the functions in problem 4, find the following:
f∘g(x) g∘f(x) g∘g(x)

7. 5 Give an algebraic expression for a graph of sin(x) that has been stretched horizontally.
 
For #2, graph it then use your graphing calculator (if you have one) to find the intersection. I got (1,6).
 
1) I'm sorry, but I don't understand the function f(x). What does "otherwise" mean? Is this piecewise, something like the following?


. . . . .\(\displaystyle \large{ f(x)\,= \,\left{\begin{array}{ll}3x\,+\,3,&x\,>\,-1\\0,&x\,\le\,-1\end{array}\right }\)


If so, then just do the graph, and write down the required information.

2) These are just straight lines. Where are you stuck with the graphing?

3) I'm sorry, but we can't see the picture you're looking at, so there is no way for us to describe the transformation it shows.

4) (f + g)(x) = f(x) + g(x); (f - g)(x) = f(x) - g(x); (fg)(x) = [f(x)][g(x)]; (f/g)(x) = [f(x)] ÷ [g(x)]. Just plug-n-chug.

5) They've given you rules for these. How far have you gotten in applying them?

6) Are these compositions? If so, then \(\displaystyle (f\circ g)(x)\,=\,f(g(x)\), \(\displaystyle (g\circ f)(x)\,=\,g(f(x))\), and \(\displaystyle (g\circ g)(x)\,=\,g(g(x))\). So plug the expression for the "inner" function inside the parentheses, and then plug that expression in for "x" every place it occurs in the "outer" function.

7) Which transformation rule corresponds to horizontal "stretching"? (Check your book and/or your notes.) Then pick any appropriate number. (There is more than one answer to this exercise.)

Eliz.
 
Emisah said:
can anyone help me with these?


1. 14 Fully describe the following function. Be sure to describe its slope, y-intercept, and the intervals over which it is increasing, decreasing, or neither.
f(x)={ 3x+3 x>−1 0 otherwise ----------- THERE

.
Click to expand...
 
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