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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 Preview

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?

a) We can observe from the definition that the function is defined for all x more than or equal to -3. Hence the domain is
b) Given that f(x)=-3 when x=0. So, y-intercept is (0, -3). Further if 2x+5=0, we get x=-5/2. Hence the x intercept is (-5/2, 0)
c)
d) the curve goes down without limit and does not cross 5. Hence the range of the function is
e) from the graph it is clear that the function is not continuous at x=0.

2. If f(x)= int(x/2) Find, (a) f(1.2) (b) f(1.6) (c) f(-1.8)
a) f(1.2)=int(0.6)=0
b) f(1.6)=int(0.8)=0
c)f(-1.8)=int(-0.9)=-1

3. Graph y= [x], then on the same screen ...

Solution Summary

Functions and their graphs are exemplified.

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