Relations and Functions
Is the following relation a function?
{(1,1), (2,4), (3,0), (5,1), (7,6)}
Yes!
There is no repetition in the domain.
What is the slope for the line
y = -7 - 3x
m = -3
Remember, slope-intercept is
y = mx + b
Write an equation for the line with slope -5 and y-intercept of 3
y = -5x + 3
Solve the system:
-7x + 4y = 24
4x - 4y = 0
(-8, -8)
Consider the sequence
-2, 1, 4, 7, ...
What is function rule that represents this sequence?
A(n) = -2 + (n - 1)(3)
What test do we perform to see if a graph represents a function?
Vertical Line Test
What is the slope of the line
y + 3 = 2(x - 1)
m = 2
Remember, point-slope is
y - y1 = m(x - x1)
y + 3 = -4(x - 2)
m = -4
point-slope form: y - y1 = m(x - x1)
Solve the system:
6x - 3y = 3
2x - y = 4
No Solution!
Does the following represent direct variation?
y + 6 = 3(x + 2)
Yes!
Solve for y, and we get:
y = 3x
Is the following relation a function?
{(0,1), (1,0), (2,3), (3,4), (5,4), (4,5), (5,6)}
No!
5 is “mapped” or “related” to two values, 4 and 6.
What is the slope of the line passing through the points
(3, 1) and (4, 3)
m = 2
What is the y-intercept of the line
y - 2 = 3(x + 4)
b = 14 or (0, 14)
Write the equation in slope-intercept form!
Solve the system:
6x - 12y = 24
-x - 6y = 4
(2, -1)
Solve the system:
2x + 4y = 8
x + 2y = 4
Infinitely many solutions!
What is the domain of the following function?
{(-2,3), (3,5), (4,2), (5,7), (7,10)}
{-2, 3,4,5,7}
What is the slope of the line passing through the points
(-2, 3) and (8, 11)
m = 4/5
Write an equation for the line parallel to y = 3x - 5 and passing through the point (-1, 1).
Point-slope form: y - 1 = 3(x + 1)
Slope-intercept form: y = 3x + 4
Solve the system:
-16 + 20x - 8y = 0
36 = -18y -22x
(0, -2)
Write an equation for the line perpendicular to 2y - 3x = 6 and passing through (-3, 0).
Point-slope form: y = -2/3(x + 3)
Slope-intercept form: y = -2/3x - 2
Evaluate f(-3) for
f(x) = -2x + 4
f(-3) = -2(-3) + 4 = 6 + 4 = 10
A ladder is leaning against a wall. The foot of the ladder is 3 feet from the wall. The top of the ladder touches the wall at a point 15 feet above the ground. What is the slope of the ladder?
rise/run = 15/3 = 5
Write the following in standard form.
y = -x/4 + 2
x + 4y = 8
Standard Form: Ax + By = C
A theater sales 78 tickets. Some tickets cost $3 and some cost $10. The theater makes a total of $486 from the sale of tickets. How many $3 tickets and how many $10 tickets were sold?
$3 tickets -> 42 tickets sold
$10 tickets -> 36 tickets sold
Consider the sequence
3, 1, -1, -3, ...
What is the 25th term in the sequence?
A(n) = 3 + (n - 1)(-2)
A(25) = 3 + (25 - 1)(-2) = 3 + (24)(-2) = 3 + -48 = -45