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
"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
"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.)"
0.2588
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.