Distance and Lines
Circles
Is it a function?
Name the Transformations
Function Composition
100
What is the distance between (3,1) and (6,5)?
5
100
What is the equation for a circle?
`(x-h)^2+(y-k)^2=r^2`
100
Is the following a function?
x y
2 0
1 -3
3 1
4 2
yes
100
What are the transformations of
`(x-2)^2 +1`
right 2, up 1
100
f(x)= 20x+ 11
g(x)= x2
find (f+g)(2)
55
200
What is the distance between (-2,6) and (4,-1)?
`sqrt85`
200
What is the center and radius?
`(x-2)^2+(y-4)^2=3^2`
center (2,4)
r=3
200
Is the following a function?
x y
-1 0
0 -3
3 1
-1 2
no, -1 has 2 different outputs
200
`2x^3-5`
Vertical stretch by factor of 2, down 5
200
f(x)= 4x+8
g(x)= 12x+10
Find (f-g)(x)
-8x-2
300
What is the line equation that passses through (3,1) and (6,5)?
y=4/3 x -3
300
What is the center and radius?
`(x+4)^2+(y-5)^2=4`
center (-4,5)
r=2
300
Is it a function? If so, what is the domain and range??
yes,
domain
`(-oo,oo)`
`"range "(-oo,0]`
300
`1/2|(x+3)|-1`
Vertical shrink/ horizontal stretch by 1/2
left 3 down 1
300
f(x)= x2+8
g(x)=
sqrtx
find (f-g)(9)
86
400
What is the line equation that passses through (-2,2) and (0,5)?
y=3/2 x +5
400
What is the center and radius of the circle?
`x^2+y^2+2x-6y=6`
`(x+1)^2+(y-3)^2=16`
Center (-1,3)
Radius 4
400
Is it a function? If so, what is the domain and range??
Not a function, doesn't pass the vertical line test
400
`-sqrt(x+2)`
reflect over x-axis, left 2
400
f(x)= 5x
g(x)=20x
find g(f(2))
200
500
You are setting up a fundraiser selling mugs for a club. You had to buy the mugs initially for $200, which will take away from your profit. You sell the mugs for $10 each.
What is the equation for profit?
How much do you make if you sell 32 mugs?
How many do you have to sell to make $500?
y=10x-200
$120
70 mugs
500
What is the center and radius of the circle?
`x^2-10y-4=-y^2-8x`
`(x+4)^2+(y-5)^2=45`
Center (-4,5)
Radius
`sqrt45 " or "6.71`
500
Is it a function? If so, what is the domain and range??
*asymptotes at x=2 and y=2
Yes,
Domain and range both
`(-oo,2)U(2,oo)`
500
`-1/4(x-2)^2+3`
reflect over x axis, vertical shrink by factor of 1/4, right 2, up 3
500
g(x) = –6x + 5
h(x) = –9x – 11
find g(h(x))
54x+71