Domain and Range
State the domain and range of the relation {(2,7),(3,10),(1,6)}$. Is it a function?
Domain:{1, 2, 3; Range:{6, 7, 10};
Yes, it is a function because each input has exactly one output.
Factor 12x² + 4x.
4x(3x + 1)
Solve 7y - 2y + 4 + 3y = -20.
y=-4
Solve n + 6 ≤ 3 and graph on a number line
n ≤ -3 (closed circle at -3, arrow pointing left)
Find the slope of the line passing through $(1, 6)$ and (3, 10).
m = 2
State the domain and range of the relation {(4,5), (5,-1), (0,12), (0,-2), (7,9)}. Is it a function?
Domain:{0, 4, 5, 7}; Range: {-2, -1, 5, 9, 12};
No, it is not a function because the input 0 has two different outputs (12 and -2).
Factor 36y² - 16.
(6y - 4)(6y + 4) or 4(3y - 2)(3y + 2)
Solve 12g - 9g + 24 - g - 9 = 13.
g = -0.5
Solve -3b - 5 ≥ -6b - 13 and graph on a number line.
b ≥ -2⅔ (closed circle at -2⅔, arrow pointing right)
Find the slope of the line passing through (-9, -11) and (6, 3).
m = 14/15
Name the quadrant where the point (-3,7) is located.
Quadrant II
Factor 81t² - 36.
(9t - 6)(9t + 6) or 9(3t - 2)(3t + 2)
Solve 5x - 9 = 11x + 3.
x = -2
Where has Mrs. Leibl lived before here?
Weyauwega, New Ulm, Omaha (NE), Oshkosh (WI)
Write an equation in slope-intercept form for the line passing through (2, -4) and (1, 6).
y = -10x + 16
Name the quadrants where the points (10,-11) and (-15,-3) are located.
(10,-11) is in Quadrant IV; (-15,-3) is in Quadrant III.
Factor x² + 14x - 15.
(x + 15)(x - 1)
Solve 1/2 p - 12 = 3/4 p - 18.
p = 24
Solve -2b > (18 - b)/5 and graph on a number line.
b < -6 (open circle at -6, arrow pointing left)
Write an equation in slope-intercept form for the line passing through (-9, 11) and (-6, -1).
y = -4x - 25
If a relation has domain {-2, 0, 3, 5} and range {1, 4, 8}, can it be a function? Explain why or why not.
Yes, it can be a function. A function requires that each input (domain value) has exactly one output (range value). There is no restriction on how many inputs map to the same output.
Factor 3x² + 28x + 32 and m² + 12m + 27.
(3x + 4)(x + 8) and (m + 3)(m + 9)
Solve 5(4x - 9) - 2x = 6x + 15.
x = 10
Carson's dad gave him $85 to spend at Kalahari. Admission is $50 and snacks cost $3 each. Write an inequality showing how many snacks Carson can buy, then solve it.
$50 + 3s ≤ 85$; $s ≤ 11⅔$; Carson can buy at most 11 snacks.
Write an equation in slope-intercept form for the line passing through (4, 2) that is perpendicular to y = -2x + 3.
y = 1/2 x