Lines and Functions
Compositions and Inverses
Graphing Polynomial Functions
Complex Numbers
100
Find an equation for the line that passes through the points (3, 2) and (4, -5).
m=(-5-2)/(4-3)=-7/1=-7
y=mx+b" "implies" "y=-7x+b" "implies" "-5=-7(4)+b"
implies" "-5=-28+b" "implies" "b=23
y=-7x+23
100
f(x)=x^2 and g(x)=2x+5
"Find "(fg)(x).
(fg)(x)=f(x)cdotg(x)=(x^2)(2x+5)
=2x^3+5x^2
100
"Using your calculator, find"
"the maximum value of y on the graph of"
y=-3x^2+7x-2.
(1.17, 2.1)
100
"Write the complex number"
7-sqrt(-36)
sqrt(-36)=sqrt(-1)cdot sqrt(36)=6i.
7 - 6i
200
Yes, because it passes the vertical line test.
200
f(x)=x^2 and g(x)=2x+5
"Find "(f@g)(x).
f(g(x))=f(2x+5)=(2x+5)^2
=4x^2+20x+25
200
Describe the left and right-hand behavior of
h(x) = -x^3+7x^2+2
Because the leading exponent is odd, and its coefficient is negative, it rises to the left and falls to the right.
200
"Multiply "(1+3i)(6-2i)
"and put the answer in standard form."
6-2i+18i-6i^2
6+16i-6(-1)" "implies" "6+16i+6
12+16i
300
"What is the slope of a line perpendicular to the line"
y=3/4x+7?
The slope of the line perpendicular is the negative reciprocal.
-4/3
300
"Find the inverse of "g(x)=sqrt(2x-3).
"inverse: "x=sqrt(2y-3)
(x)^2=(sqrt(2y-3))^2" "implies" "x^2=2y-3
y=1/2x^2+3/2
300
"Divide "(x^3-3x^2-25x-21)div(x+3)
Use long division or synthetic division.
x^2-6x-7
300
"Write "(2+i)/(3-i)" in standard form."
((2+i))/((3-i))cdot((3+i))/((3+i))=(6+2i+3i+i^2)/(9-i^2)=(6+5i+(-1))/(9-(-1))=(6+5i-1)/(9+1)=(5+5i)/10
1/2+1/2i
400
"Given "f(x)=(x^2+1)/(x+3)
"find the value of "f(-7).
f(-7)=((-7)^2+1)/(-7+3)=50/-4=-25/2
500
"How does the graph of"
f(x)=root(3)(x+5)
"differ from the graph of"
f(x)=root(3)(x)?
f(x)=root(3)(x)" is shifted 5 units left."