Relations
What is the domain of {(1, 4), (2, 5), (3, 6)}?
{1, 2, 3}
Is {(1, 2), (2, 3), (1, 5)} a function? Explain.
No, the input 1 has two outputs (2 and 5)
Complete the table for y = 2x + 1:
x: −1, 0, 1, 2
y: ?
y: −1, 1, 3, 5
Find the slope of the line through (1, 2) and (3, 8).
m = 3
Solve: 3x + 7 = 22
x = 5
What is the range of {(−2, 3), (0, 3), (4, −1), (5, 7)}?
{−1, 3, 7}
If f(x) = 3x − 4, find f(5).
f(5) = 11
Find the x- and y-intercepts of x + y = 6.
x-int (6, 0); y-int (0, 6)
Find the slope of the line through (−2, 5) and (4, 2).
m = −1/2
Evaluate 2x2− 3x when x = −2.
14
A mapping diagram shows: 1 → 4, 2 → 4, 3 → 6. Write the relation as ordered pairs and state the domain and range.
{(1, 4), (2, 4), (3, 6)}
Domain {1, 2, 3}, Range {4, 6}
If f(x) = x2− 2x + 1, find f(−3).
f(−3) = 16
Complete the table for y = −3x + 4 for x = −2, 0, 2. Which point is the y-intercept?
y: 10, 4, −2
y-intercept (0, 4)
A taxi charges $3 plus $2 per mile. What is the rate of change, and what does it mean?
$2 per mile, the cost rises $2 for each mile driven.
Solve: 5(x − 2) = 3x + 8
x = 9
State the domain and range of the relation in the table:
x: −1, 0, 1, 2
y: 3, 3, 5, 7
Domain {−1, 0, 1, 2}
Range {3, 5, 7}
If g(x) = −2x + 7, find x when g(x) = −5.
x = 6
Find the x- and y-intercepts of 3x − 4y = 12.
x-int (4, 0); y-int (0, −3)
Hours: 1, 3, 5, 7
Cost ($): 20, 32, 44, 56
Find the rate of change. Is it constant?
$6 per hour; yes, it is constant (linear).
x=4 or x=-6
For y = x2
with domain {−2, −1, 0, 1, 2}, list the ordered pairs and state the range.
(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4)
Range {0, 1, 4}
f(x) = 3x + b and f(2) = 11. Find b, then find f(−4).
b = 5; f(−4) = −7
x: 0, 2, 4, 6
y: 9, 6, 3, 0
Name the x- and y-intercepts, then write the equation of the line.
x-int (6, 0); y-int (0, 9)
y = −(3/2)x + 9
Find k so that the line through (2, k) and (5, 11) has slope 3.
k = 2
Solve: 2|x-1|+3<11
-3<x<5