Pre-Calc Benchmark 2

• When a function has a negative exponent, you can flip the fraction. ex. 3x^-2 -> 3/x^2
• Vertex: point where the direction changes in the graph.
• To solve a radical equation, isolate the square root and get rid of it. Make sure to check for extraneous solution.
• Polynomials: many terms.
• If the remainder is 0, the quotient and the divisor are the factors of the polynomial.
• When doing long division, always check if you have zero placement.
• If the quotient is more factorable, factor it.
• Synthetic division is only possible when the divisor is a binomial.
• To find vertical asymptote, factor the equation, then cross out any same factors, then use the denominator and solve.
• To find horizonal asymptote, take highest degree variables of both numerator and denominator. If x is left in the denominator HA = 0, if x is left in the numerator, HA does not exist.
• When the domain is an imaginary number, the domain is all real numbers.
• To solve a rational equation, factor numerator and denominator and cancel if possible. Find LCD and multiply each term by LCD to get rid of denominators.
• An exponential function is 4^x.
• A power function is x^4
• Parent functions typically do not have an x-intercept unless they are translations.
• f(x)+c = shift upward c units.
• f(x)-c = shift downward c units.
• f(x+c) = shift to the left c units.
• f(x-c)= shift to the right c units.
• -f(x) = reflect over x-axis.
• f(-x) = reflect over y-axis.
• a * f(x), when a>1 = stretch vertically by a factor of a.
• a * f(x), when 0<a<1 = shrink vertically by a factor of a.
• f(a*x), when a>1 = shrink horizontally by a factor of a.
• f(a*x), when 0<a<1 = stretch horizontally by a factor of a.
• Compound Interest: A=P(1+r/n)^nt
• Continuous Compound Interest: A=Pe^rt
• Exponential Growth or Decay: N=No(1+r)^t
• Continuous Exponential Growth or Decay: N=Noe^rt
• If the base of log is not given, it is understood as 10.
• The log of a negative number is undefined.
• Change of Base: log(x)/log(b)
• Expanded form has no coefficients.
• Turning Point is one less than the highest degree variable.
• (1+r/n) = Growth Factor
• When r>0, it has a growth rate.
• When r<0, it has a decay rate.