Solving Equations & Inequalities
What inequality shows a number line that has a filled in circle at -4 and goes left?
x <= -4
Is a circle a function? Why or why not?
NO! It will fail the vertical line test.
Find the slope between (-1, 5) and (3, 8)
m = 3/4
Solve the system: y = -3x and y = 5x + 16
(-2, 6)
What is the vertex and is it a max/min: y = -1/2x^2 + 2x - 4
Max (2, -2)
Solve: 1/2 (12x - 7) = 3/5
x = 41/60
Is this set of points a function? Why or why not? (2,2) (3,4) (3,6)
Yes - every x has exactly one y value
What line is parallel to 2x - y = 7 and has a y-intercept of 8?
y = 2x + 8
b^12 / a^6
Factor: 2x^2 - 32
2(x^2 - 16)
2(x - 4)(x + 4)
Name 3 solutions for: -2 < x - 6 <= 5
4 < x <= 11
Possible solutions: 4.2, 6, 10.33, 11
If g(x) = -3x^2 - 4 find g(-2)
-16
Convert to SIF, then describe how you would graph: x - 5y = 153
y = 1/5x - 3
Start by graphing a y-int of -3. From there, go up 1 right 5.
Is (-2, -13) on the graph of y = -x^2 + 5x - 9
NO... y = -4 - 10 - 9 = -23 --> (-2, -23) is on the line
Factor: 3x^2 + 21x - 24
3(x - 1)(x + 8)
Solve: -15 < -3(5 - x) - 4x
x < 0
[2, infinity]
What line is perpendicular to 3y = x + 14 and goes through (2, 0)?
y = -3x + 6
Solve the system: 3x = 3y - 3 and x - y = 12
No solution
y = 1(x + 1)^2 - 4
Solve: -3 - |x + 2| = -18
x = -17 or 13
If a(x) = -10 - 6x find x if a(x) = 7
x = 17/-6 or -17/6 or -2 5/6
Write the equation in standard form that goes through (-2, 4) and (-3, 7).
SIF: y = -3x - 2
SF: 3x + y = -2
Simplify: (-4 a^4 b^-2)^3 / (-2ab^-6)^2
-16 a^10 b^6
The area of a rectangle with length (x - 2) and width (x - 1) is 20 m^2. Solve for x and find the dimensions.
x = 6, and it is 4m x 5m