Pre-Calc Benchmark 2

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    Created by
    Anita M.

    Cards (37)

    • 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.
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