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Relations & Functions + Rationals & Radicals
Polynomials
Factoring Polynomials
Rational Expressions
Quadratic Equation
100
What is the difference between a relation and a function?
A function is a relation in which each value in the domain (x) has a unique value in the range (y). The x's don't repeat, but the y's may.
100
Add and simplify. (2x^2 - 11x) + (3x^2 + 10x - 4)
5x^2 - x - 4
100
Simplify the fraction in Pic 5.12.2
(2/3)a^2b
100
What is the restriction for the variable? (3y^2 - 3y) over (y - 3)
y cannot equal 3
100
What value should be added to the expression to create a perfect square? x^2 - 10x
25
200
f(x) = 2 - 3x Evaluate f(-4)
14
200
Subtract and simplify. (3x^2 + 7) - (x^2 - 6x - 4)
2x^2 + 6x + 11
200
Factor. 3x + 27x^2
3x(1 + 9x)
200
Multiply the two fractions in Pic 5.12.3
(2a^3)/7
200
Solve. x^2 + 8x + 10 = 0
-4 + sqrt 6 and -4 - sqrt 6
300
Simplify completely the square root of (18x^8)
3x^4 square root of 2
300
Multiply and simplify (-3x^2y^2) * (y^4x^3)
-x^5y^6
300
Simplify. Assume the divisor is not zero. (4x^2y^2 - 4xy) divided by 4xy
xy - 1
300
What is the restriction on the domain in Pic 5.12.4?
x cannot equal -9 or 0
300
Solve. Use the quadratic formula. Write solution in simplest radical form. 2x^2 + 2x - 1 = 0
(-1 + sqrt 3)/2 and (-1 - sqrt 3)/2
400
Approximate square rot of 500 to the nearest tenth
22.4
400
What is the perimeter of the triangle in Pic 5.12.1 expressed as a polynomial?
11x - 2
400
Factor v^2 - 16
(v + 4)(v - 4)
400
Subtract and simplify the fractions in Pic 5.12.5
(x + 5)/(x - 5)
400
How many real-number roots does the equation have? Use the discriminant. 3x^2 - 6x + 4 = 0
no real-number roots
500
Solve for x. 3x^2 - 75 = 0
x = 5, -5
500
Multiply the binomials using the FOIL method. (b - 3)(b + 9)
b^2 + 6b - 27
500
Factor completely. 3x^3 - 27x
3x(x - 3)(x + 3)
500
Subtract and simplify the fractions in Pic 5.12.6
Pic 5.12.7
500
Without drawing the graph of the equation answer the question. How many points does the given equation have in common with the x-axis and where is the vertex in relation to the x-axis? y = -2x^2 + x - 3
no points in common; vertex is below the x-axis