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Functions and their graphs

1. f(x)= 2x+5 if -3 <= X <0
-3 if x=0
-5x if x>0

a. Find the domain of each function.
b. Locate any intercepts.
c. Graph each function
d.Based on the graph find the range.
e. Is f continuous on its domain?

2. If f(x)= int(x/2) Find, (a) f(1.2) (b) f(1.6) (c) f(-1.8)

3. Graph y= [x], then on the same screen graph y=2[x],followed by y=4[x],followed by Y=1/2[x]. what pattern do you observe?Can you predict the graph of Y=1/4[x]? Of Y=5[x]?

[x] = Absolute X.

4. Find the function that is finally graphed after the following transformation are applied to the graph of Y= square root of X.
(a) Reflect about x-axis
(b) shift right 3 units.
(c) Shift Down 2 units.

5. If (3,6) is a point on the graoh of Y=f(x) which of the following point must be on the graph of Y=f(-x).
(a) (6,3)
(b) (6,-3)
(c) (3,6)
(d) (-3,6)

6. Suppose that the function Y=f(x) is decreasing on the interval (-2,7).
(a) Over what interval is the graph of Y=f(x+2) decreasing.
(b) Over what interval is the graph of Y=f(x-5) decreasing.
(c) What can be said about the graph of Y= -f(x).
(d) What can be said about the graph of Y= f(-x).

7. Graph each function using the technique of shifting,compressing,stretching and or reflecting. Start with graph of the basic function ( for example Y=x^2) and show all the stages. Be sure to show atleast 3 key points. Find the domain and range of each function.

f(x)= 3(x-2)^2 + 1.

8. f(x)= -3x^2 + 5x
(a). Is the point (-1,2) on the graph of f.
(b) If x= -2, what is f(x)? What the point is on the graph of f.
(c) If f(x)= -2, What is x? What point are on the graph of f.
(d) what is the domain of f.
(e) List the x intercepts in any of the graph of f.
(f) List the y intercept, if there is one, of the graph of f.

Solution Summary

Functions and their graphs are exemplified.