Math 110 Exam 1
Finding Domain - Answers -Rule 1) Cannot divide by zero
set denominator to zero and solve
Finding Domain - Answers -Rule 2) cannot take the square root of negative number
set what is inside radical >= 0 and solve
*make number lines*
Polynomial Function - Answers -ex: f(x)= 2x^4 + 3x^2 - 10x
all powers must be *non negative whole numbers* cannot have negative powers,
square roots, or fractional powers
the *degree* of the function is the highest power (in this case 4)
Rational Function - Answers -ex: f(x)= (x^3 +5x^2 -7) / x+1
It is the QUOTIENT of 2 polynomials
This means NO negative powers, square roots or fractional powers
*does NOT have a degree*
Power Function - Answers -ex: f(x)= 2x^5, 3x^-2, square roots, etc
Powers can be any real number (including negatives and fractions)
*does NOT have a degree*
All polynomial functions are power functions... - Answers -but the reverse is not true!
Not all power functions are polynomial functions
Equilibrium Point - Answers -occurs where the supply function equals the demand
function
s(x) = d(x)
To find equilibrium *quantity* - Answers -set s(x)=d(x) and solve for x
Finding Domain - Answers -Rule 1) Cannot divide by zero
set denominator to zero and solve
Finding Domain - Answers -Rule 2) cannot take the square root of negative number
set what is inside radical >= 0 and solve
*make number lines*
Polynomial Function - Answers -ex: f(x)= 2x^4 + 3x^2 - 10x
all powers must be *non negative whole numbers* cannot have negative powers,
square roots, or fractional powers
the *degree* of the function is the highest power (in this case 4)
Rational Function - Answers -ex: f(x)= (x^3 +5x^2 -7) / x+1
It is the QUOTIENT of 2 polynomials
This means NO negative powers, square roots or fractional powers
*does NOT have a degree*
Power Function - Answers -ex: f(x)= 2x^5, 3x^-2, square roots, etc
Powers can be any real number (including negatives and fractions)
*does NOT have a degree*
All polynomial functions are power functions... - Answers -but the reverse is not true!
Not all power functions are polynomial functions
Equilibrium Point - Answers -occurs where the supply function equals the demand
function
s(x) = d(x)
To find equilibrium *quantity* - Answers -set s(x)=d(x) and solve for x
