Zeros
`"Use the Rational Zero Test to list all possible rational zeros of"`
`f(x)=2x^3-2x^2+x-8`
`pm8,pm4,pm2,pm1,pm1/2`
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`"State the domain of "f(x)=(x+3)/(x^2-16)`
`f(x)=(x+3)/((x-4)(x+4))`
`D=(x|xne4 or -4}`
`"Evaluate the expression "-12(3^-0.2) "using your calculator."`
`"(Round to 2 decimal places.)"`
-9.63
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`"What is the maximum value for"cos theta?`
1
`"Find all real zeros of the function "f(x)=x^4-x^3-6x^2.`
`f(x)=x^4-x^3-6x^2" "implies" "f(x)=x^2(x^2-x-6)`
`f(x)=x^2(x-3)(x+2)`
`"The zeros are "0, 3, and -2."`
`g(x)=(x-7)/(x+6)" State the x-intercept if it exists."`
`"Let "g(x)=0 " and solve " 0=(x-7)/(x+6)`
`(7,0)`
`"Evaluate "log73" using your calculator."`
`"(Round to 4 decimal places.)"`
1.8633
`"If "costheta" is positive, and"tantheta" is negative, what quadrant is " theta" in?"`
`"If "costheta" is positive, then "theta " must be in quadrant I or IV. "`
`"If "tantheta" is negative, "theta" must be in quadrant II or IV. "`
`" So, " theta" must be in quadrant IV."`
`g(x)=(x-7)/(x+6) " State the y-intercept if it exists."`
`"Let x=0 and solve."`
`(0,-7/6)`
`"Expand the expression "log7x^4" as a sum, difference, and/or multiple of logarithms."`
`log7+logx^4`
`log7+4logx`
`"Use your calculator to evaluate"sin(pi/12).`
`"(Round your answer to 4 decimal places.)"`
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`0.2588`
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Find all of the zeros of
`f(x)=x^4+x^3+7x^2+9x-18`
`f(x)=(x-1)(x+2)(x^2+9)" "implies" "x^2+9=0" "implies" "x^2=-9" "implies" "x=pm3i`
`"The zeros are "1, -2, 3i, -3i`
`g(x)=(x-7)/(x+6)
" State the vertical asymptote if it exists."`
`"The vertical asymptote happens at the value that makes the function undefined."`
`"The vertical asymptote is the line "x=-6`
`"Condense the expression "1/3lnx-2ln(x-7) " to the logarithm of a single quantity."`
`lnx^(1/3)-ln(x-7)^2" "implies" "ln(root(3)(x))-ln(x-7)^2`
`ln((root(3)(x))/((x-7)^2))`
`"Use your calculator to evaluate "csc20^o.`
`"(Round to 4 decimal places.)"`
`csc 20^o = 1/(sin 20^o)=2.9238`
`"Identify the horizontal asymptote of "f(x)=(3x^3+4x^2)/(x^3+2x)`
`"To determine the horizontal asymptote, see what the leading term of the numerator and denominator simplify to."`
`f(x)=(3x^3)/(x^3)" "implies" "y=3/1" "implies" "y=3" is the asymptote."`
`"Solve the equation "e^(2x)=12.`
`"Approximate your answer to 3 decimal places."`
`" "`
`ln(e^(2x))=ln(12)`
`2x=ln12 " "implies" "x=ln12/2`
`x=1.242`
`"Find"sintheta" if"sectheta=5/3 and tanthetalt0.`
`"If "sectheta=5/3" then "costheta=3/5". Since "costheta" is positive, "theta" is in quadrant I or IV."`
` "Since "tanthetalt0", "theta" must be in quadrant IV."`
`"If "costheta=3/5", then "sintheta=-4/5.`