Vocabulary
Definition: The values of x that make a polynomial or function equal to zero; where the graph crosses or touches the x-axis.
Simplify: (2x² + 3x) + (4x² − 5x)
What is 6x² − 2x
Simplify: i²
What is −1
Simplify: √49
What is 7
Is the function f(x) = 2(1.05)x growth or decay?
What is growth?
Definition: A solution that appears during solving but does not satisfy the original equation.
What is an extraneous solution?
Factor: x² − 9 into the product of two binomials
What is (x + 3)(x − 3)
Simplify: (3 + 2i) + (1 − 5i)
What is 4 − 3i
Simplify: x³ ⋅ x⁴
What is x⁷
Fill in the blanks:
In f(x) = 100(0.94)x
0.94 represents a ________ of 6 percent per year
Definition: A line that a graph approaches but never touches, common in rational or exponential functions.
What is an asymptote?
Describe the end behavior of:
f(x) = −2x³ + x² − 5
As x -> +infinity, y -> -infinity
As x-> -infinity, y-> +infinity
Simplify: (2 + 3i)(2 − 3i)
What is 13
Simplify: (27x⁶)1/3
What is 3x²
Write the general formula for exponential growth.
What is y = a(b)x
In a radical expression, this number tells you which root is being taken.
What is the index?
Divide: (2x³ − 3x + 4) ÷ (x + 1)
What is 2x² − 2x − 1, remainder 5
Simplify: (1 + 2i)(3 + 4i)
What is −5 + 10i
Simplify: (16x⁸)1/4
What is 2x²
A population triples every 5 years. Write a formula if the starting value is 500.
What is P(t) = 500(3)t/5
The number of times a root is repeated in a polynomial.
What is multiplicity?
State the degree and leading coefficient of: f(x) = 5x⁴ − 2x³ + x
Degree: 4, Leading Coefficient: 5
What are the solutions to this quadratic equation?
y = 4x3 + 5x + 7
x = (-5 +- isqrt87)/8
Rationalize the denominator: 5 / √2
What is (5√2) / 2
Solve for x: 200(1.02)x = 300
What is x ≈ 20.1