REVIEW STATION 1
(Functions)
1. Find the domain of
x 1
10 x  13x  3
2
2. Determine whether the equation defines y as a function of x (Yes or No)
3
y=x
3. For f(x) = 3x 3 – 2x 2 – 6 and g(x) = x 2 + 3, determine the following:
g ( x  h)  g ( x )
a) f – g
b) f  g
c) the difference quotient:
h
REVIEW STATION 2
(Distance and Midpoint)
1. Use the midpoint formula to determine the other endpoint if (6, 2) is the endpoint
of a line segment and (1, -1/2) is the midpoint.
2
2. What is (3 2 ) ?
3. Find all points having x coordinate of 9 whose distance from point (3, -2) is 10
4. The medians of a triangle are the line segments from each vertex to the midpoint
of the opposite side (see the figure). Find the equation of the line segment ON in
slope intercept form. A = (0, 0) B = (6, 0) C = (4, 4)
N
A
B
O
5. Find all points on the x-axis that are 5 units away from (-1, 3)
6. Show if the points A (3, 4) , B(1, 1) and C (-2, 3) are the vertices of an isosceles
triangle.
REVIEW STATION 3
(Lines and circles)
1.
a)
b)
c)
Suppose (-3, -2) and (3, 6) are the endpoints of the diameter or a circle
Find the distance between the 2 points.
Find the midpoint of the line connecting the 2 points.
Find the general form equation of the circle containing the 2 points
2. Determine the a) standard form and b) general form equation of a circle with center
(4, 3) that is tangent to the x-axis.
3. Determine the equation of the line perpendicular to 2y – 4x = 6 containing the point
(1, -2) and express in
a) slope-intercept form
b) point-slope form
c) general form
4. Find the coordinates (x, y) of all intercepts
-4x + 5y = 40
5. Solve by completing the square using no decimals, and showing all work:
x 2 + 5x + 3 = 0
REVIEW STATION 4 - (Functions and circles)
1. Determine f(x – 3) when f(x) = 3x 2 + 2x -1
2. Is y a function of x? y 2 = 4 - x 2
1
x 1
f
and ( )(x) = 2
, a) find the function g (what is g?) and
x
x x
g
f
b)what is the domain of ( )(x)?
g
4. Find the equation of the lines in slope-intercept form that connects the centers of
the 2 given circles:
3. Given f(x) =
x 2 + y 2 + 4x – 4y – 1 = 0 and x 2 + y 2 – 6x + 2y + 9 = 0
5. For f(x) =
x2
, determine f(-3)
x  2x  5
2
6. Determine the intercepts of y = 3x 2 + 14x – 5
REVIEW STATION 5 - (Functions)
1. Find the difference quotient of f(x) = -2x 2 + x + 1
f ( x  h)  f ( x )
Difference Quotient :
h
2
2. f(x) = -3x + 5x
a) Is the point (-1, 2) on the graph of f(x)?
b) If x = -2, what is f(x)? What is the POINT on the graph of f?
c) If f(x) - -2, what is x? What point(s) are on the graph of f?
d) What is the domain of f?
e) List the x-intercepts, if any, on the graph of f
f) List the y-intercepts, if any, on the graph of f
3.
Find the domain of
x2 1
x2  9
4. Factoring review (yes! You may see one of these on the test!)….Factor
completely, simplify your answer, but leave in factored form:
2(3x+4) 2 + 6(3x + 4)(2x +3)
5. Simplify:
4
x9 y 7
xy 3
REVIEW STATION 6 - (Mixed Review)
1. Determine whether each relation represents a function:
a) { (2, 6), (-3, 6), (4, 9), (2, 10)}
b) { (-4, 4), (-3, 3), (-2, 2), (-1, 1), (-4, 0)}
2x  3
4x
and g(x) =
3x  2
3x  2
a) find f – g AND state the domain
f
b) find AND state the domain
g
3. State the domains of these functions:
2. f(x) =
3x  12
a) 3
b)
x
2
x 1
4. Give the equation of a) the vertical line and b) the horizontal line passing through the
point (-3, 2). List the slope of each line.
2
REVIEW STATION 7
(Mixed Review)
1. f(x) = 2x 2 – 3x, evaluate for the difference quotient:
f ( x  h)  f ( x )
h
2. Determine f(x – 1) when f(x) = 5x 2 + 2x -1
3. Find the domain of
4x 2
2x  1
3x 2  2x - 5
4. For f(x) =
, find
x2
a) the coordinates (x, y) of all intercepts
b) value(s) of x to make f(x) = 8
2
5. What is (2 5 ) ?
6. If a right triangle has c = 8 and b = 5, what is a?