Transcript Notes Over 2.2 Identifying Functions

Notes Over 2.2
Identifying Functions - Numerically
Decide whether the relation is a function.
1. Input Output
2. 1, 4, 1, 2, 3, 4, 5,  4
2
1
A function, because every
4
3
input goes to only one output
5
8
7
Not a function, because 4
goes to both 3 and 5
Notes Over 2.2
Identifying Functions - Verbally
Decide whether the relation is a function.
3. In a school basketball game, all ticket prices are the
same. The input value x is the number of tickets
purchased, and the output y is the total price paid.
A function, because every input goes to only one output
4. The input value x is the number of times you cast your
line in fishing, and the output y is the total number of
fish caught.
Not a function, because you could throw your line in 5
times one day and catch 2 fish and another day throw it in
5 times and not catch anything.
Notes Over 2.2
Identifying Functions - Graphically
Decide whether the relation is a function.
5.
Vertical line test
1
1

2

3
2
2
A function, because
it only hits the graph
once all the way
across.
Notes Over 2.2
Identifying Functions - Graphically
Decide whether the relation is a function.
6.
Vertical line test
Not a function,
because it hits the
graph more than
once from -5 to 5.
Notes Over 2.2
Identifying Functions - Algebraically
Decide whether the relation is a function.
7. x  y  17
Try to solve for y
y   x  17
A function, because every input goes to only one output
8. y  x  17
y   x  17
y   x  17
y  x  17
Not a function, because most inputs will have 2 outputs
Notes Over 2.2
Identifying Functions
9. f x   9 x  2 Find f(-2), f(5), and f(x - 3)
f  2  9 2  2  18  2  16
f 5  95  2  45  2  47
f x  3  9x  3  2  9x  27  2
 9 x  25
Notes Over 2.2
Evaluating a Piecewise Function
Evaluate the function for the given value of x.
 x  1, if x  1
f x   
 x  2, if x  1
10. f 1
 x2
 1  2
3
11. f 3
x 1
3  1
4
Notes Over 2.2
Finding the Domain of a Function
Find the domain of each function.
1
f x   2
x 9
f x   x  3
x5
12. f  x  
x7
Domain excludes x-values
that result in division by 0.
Domain excludes x-values
that result in even roots of
negative numbers.
All real numbers
x7
Notes Over 2.2
Finding the Domain of a Function
Find the domain of each function.
13. f x   x  16
2
x  16  0
x  4x  4  0
Closed Circles
l
-6
l
l
-4
l
l
-2
l

l
0
4
4
2
These are critical values
l
l
2
l
 ,  4  4, 
l
4
l
l
6
Notes Over 2.2
Function Application
14. Andre Agassi hit a lob in tennis right on his baseline that
took a path given by the function:
f x   0.015625 x  1.25 x  3
2
where x and y are measured in feet. If a tennis court is 78
feet long, will the ball land in, assuming he hit it straight?
f x   0.01562578  1.2578  3
f x  5.4375
2
No, because it is still
coming down.
Notes Over 2.2