Graphs
Is the relation a function?
[(1,2),(2,3),(3,4),(1,5)]
No (x=1 repeats)
Is the equation a polynomial? If so, state the degree:
f(x)=5x3-2x+7
Yes, it is a polynomial
Degree = 3
Solve for x:
5x-12=8
x = 4
Factor:
x2+9
(x-3)(x+3)
Solve:
2x-5>3
x>4
Write in slope-intercept form:
slope = 3, through (2, −1)
y=3x−7
Identify the degree, terms, and coefficients:
4x4-3x2+8x-1
Degree = 4
Terms = 4x4, -3x2, 8x, -1
Coefficients = 4,-3,8,-1
Solve for x:
5+3(x-4)=7x-9
x = 1/2
Factor:
3x2-12x
3x(x-4)
Evaluate:
f(x)=2x3-5x+1
f(2) =
f(-1) =
f(2) = 7
f(-1) = 4
Write in point-slope form:
slope = −2, through (5, 4)
y−4=−2(x−5)
Add:
(2x2-3x+5)+(x2+4x-7)
3x2+x-2
Solve for x:
x2-7x+10=0
x=2 and 5
Multiply using FOIL:
(2x+3)(x+6)
2x2+15x+18
Solve using the Quadratic Formula:
3x2-5x-2=0
x = 2 and -1/3
Find the x and y intercepts:
2x+3y=12
x=6, y=4
Subtract:
(5x3-2x+7)-(3x3+4x-2)
2x3-6x+9
Solve using Square Root Property:
(x+4)2=36
x = 2, x = -10
Factor:
x2-11x+30
(x-5)(x-6)
Determine if the equation is even or odd and state the symmetry:
f(x)=x3-x
Odd, symmetry about the origin
Describe the transformations:
y=x2 to y=-2(x-3)2+4
Shift right 3, reflect over x-axis, vertical stretch by 2, shift up 4
Add:
(4x5-3x4+12x3-8x2-x+2)+(6x6+5x5+3x4-3x3+7x2+2x-2)
6x6+9x5+9x3-x2+x
Solve and write in interval notation:
-4x+5>1
x<1, interval: (-∞,1)
Multiply using FOIL:
(4x-3)(2x-7)
8x2-34x+21
Find the difference quotient:
y=2x2-3x+1
4x+2h-3