Transcript UNIT III Algebra 1 Section 4-6 Functions

Warm Up
Evaluate each expression for a = 2, b = –3,
and c = 8.
1. a + 3c 26
2. ab – c
–14
3.
1c + b 1
2
4. 4c – b 35
5. ba + c 17
Solve each equation for y.
6. 2x + y = 3 y = –2x + 3
7. –x + 3y = –6
8. 4x – 2y = 8
y = 2x – 4
4-6: Functions
A function is a special type of
relation that pairs each domain
value with exactly one range
value.
In other words, for every input
(x value), there is exactly one
output (y value).
Example 1: Identifying Functions
Give the domain and range of the relation. Tell
whether the relation is a function. Explain.
{(3, –2), (5, –1), (4, 0), (3, 1)}
D: {3, 5, 4}
R: {–2, –1, 0, 1}
Even though 3 is in the domain twice,
it is written only once when you are
giving the domain.
The relation is not a function. Each domain value
does not have exactly one range value. The domain
value 3 is paired with the range values –2 and 1.
Additional Example 1B: Identifying Functions
Give the domain and range of the relation. Tell
whether the relation is a function. Explain.
X
–4
–8
4
5
Y
2
1
Use the arrows to determine
which domain values correspond
to each range value.
D: {–4, –8, 4, 5}
R: {2, 1}
This relation is a function. Each domain value is
paired with exactly one range value.
Example 1c
Give the domain and range of each relation. Tell
whether the relation is a function and explain.
X
a. {(8, 2), (–4, 1),
(–6, 2),(1, 9)}
D: {–6, –4, 1, 8}
R: {1, 2, 9}
The relation is a
function. Each domain
value is paired with
exactly one range
value.
Y
b.
D: {2, 3, 4}
R: {–5, –4, –3}
The relation is not a
function. The domain
value 2 is paired with
both –5 and –4.
Mini Lesson Quiz: Part I
3. Give the domain and range of the relation.
Tell whether the relation is a function. Explain.
X
Y
D: {5, 10, 15};
R: {2, 4, 6, 8};
The relation is not a
function since 5 is paired
with 2 and 4.
What is the “Vertical Line
Test” ?
Example 2A
The three points below form a straight line, thus this
appears to be the graph of a linear function.
Use the vertical line test on the graph.



No vertical line will intersect the
graph more than once. The
equation –3x + 2 = y represents
a function.
Example 2B
The points below appear to form a V-shaped
graph. Draw two rays from (0, 2) to show all the
ordered pairs that satisfy the function. Draw
arrowheads on the end of each ray.
Use the vertical line test on the graph.



No vertical line will intersect the
graph more than once. The
equation y = |x| + 2 represents a
function.
Reading Math
Functions can be named with any letter; f, g, and
h are the most common. You read f(6) as “f of 6,”
and g(2) as “g of 2.”
Evaluation of Functions: Example 4
Evaluate the function for the given input values.
For h(c) = 2c – 1, find h(c) when c = 1 and
when c = –3.
h(c) = 2c – 1
h(1) = 2(1) – 1
h(c) = 2c – 1
h(–3) = 2(–3) – 1
=2–1
= –6 – 1
=1
= –7
Example 4b
Evaluate each function for the given input
values.
4. For g(t) =
t = –12.
g(20) = 2
g(–12) = –6
find g(t) when t = 20 and when
5. For f(x) = 6x – 1, find f(x) when x = 3.5 and when
x = –5.
f(3.5) = 20
f(–5) = –31