Functions
Properties of Function Graphs
Linear Functions and Slope
Parallel and Perpendicular Lines
Transforming Functions
Composite and Inverse Functions
Distance, Midpoint, and Circles
100
Determine whether or not the following set of points represents a function.
{(1,4),(1,5),(1,6)}
No!
100
How many maximum & minimum points are visible?
2 Maximum Points
2 Minimum Points
100
Write the equation of a line with slope -3 passing through the point (-2, -5) in point-slope form.
y+5=-3(x+2)
100
What is the slope of a line parallel to
y=-3/2x+9
Slope=-3/2
100
Name the family to which this function belongs and describe its transformation(s).
(x-1)^2+3
Quadratic Family
Right 1 unit
Up 3 units
100
Given f(x)=3x-2 and g(x)=9x+5, find f(g(8)).
203
100
Find the midpoint of the line segment with the endpoints (6, 8) and (2, 4).
(4, 6)
200
Determine which graphs represent a functions.
Graph a: Yes
Graph b: Yes
Graph c: No
200
Where is the location of each max & min?
Maximum: (-1, 2) and (4, 5)
Minimum: (-3, -2) and (2, -6)
200
Find the slope between (-2, 4) and (-1, -1).
Slope = -5
200
What is the slope of a line perpendicular to the line
y=7x-12
slope=-1/7
200
Name the family to which this function belongs and describe its transformation(s).
4sqrt(-x+1)
Square Root Family
Stretch by a factor of 4
Reflect about the y-axis
Left 1 unit
200
Given
f(x)=3-x^2 and g(x)=x^2+2x-15
find g(f(4)).
-78
200
Find the distance between the point (0, 0) and (-3, 4). If necessary, keep your answer in simplified form (no decimals!)
5
300
Given the following function, find
f(-6)
f(x)=sqrt(x+6)+3
x=3
300
On which intervals is x increasing and decreasing?
Decreasing: [-4, -3], [-1, 2], [4, 5]
Increasing: [-3, -1], [2, 4]
300
Find the equation of the line between (-3, -2) and (3, 6) in point-slope form.
y+2=4/3(x+3)
y-6=4/3(x-3)
300
Write the equation in point-slope form of the line passing through the point (-8, -10) and parallel to the line
y=-4x+3.
y+10=-4(x+8)
300
Name the family to which this function belongs and describe its transformation(s).
y=-1/5(x+6)^3-8
Cubic Family
Reflect about the x-axis
Compress by a factor of 1/5
Left 6 units
Down 8 units
300
Find the inverse of the function
f(x)=4x-8
y^-1=1/4x+2
300
Find the distance between the point (0, -3) and (4, 1). If necessary, keep your answer in simplified form (no decimals!)
4sqrt2
400
Given the following function, find f(30).
f(x)=0.012x^2-0.2x+8.7
f(30)=13.5
400
Write the domain and range of the function.
Domain:[-4,5] or {x|-5 < x
5}
Range: [-6, 5] or {y|-6 y 5}
400
Write the equation between the points (3, 5) and (8, 15) in slope-intercept form.
y=2x-1
400
Write the equation of the line in slope-intercept form that passes through the point (2, -3) and perpendicular to
y=1/5x+6.
y=-5x+7
400
Graph the function
y=-sqrt(x+3)+2
See Board
400
Find the inverse function of
f(x)=(x+8)^2-4
y^-1=sqrt(x+4)-8
400
For the following circle, state the location of the center and the radius.
Then graph the circle and state the domain and range.
(x+2)^2+(y-3)^2=49
Center: (-2, 3)
Radius: 7
Domain: [-9, 5]
Range: [-4, 10]
500
State the domain and range of the function.
Domain:(-2, 2] or {x|-2 < x2}
Range: [-5, 4] or {y|-5 y 4}
500
On the same graph, graph the following function with the restricted domains.
y=-3 if -3x3
x=-3 if -3y--1
x=3 if -3y-1
y=3 if 2x4
y=3 if -4x-2
See Picture
500
Write the equation of the line in slope-intercept form with an x-intercept at 4 and a y-intercept at -2.
y=1/2x-2
500
Write the equation of the line in slope-intercept form that is perpendicular to the line 3x-2y-4=0 and also has the same y-intercept.
y=-2/3x-2
500
Graph the function
y=1/2(-x-4)^3
See Board
500
Find the inverse of the function
f(x)=(2x-3)/(x+1), x
-1
y^-1=(-x-3)/(x-2)
500
In the graph below, a line segment through the center of the circle intersects the circle at the points (3, 6) and (11, 8).
a. Find the coordinates of the circle's center.
b. Find the radius of the circle.
c. Use this information to write and equation of the circle in standard form.
a. Center: (7, 7)
b. Radius =
sqrt17
c. Equation
(x-7)^2+(y-7)2=17