Precalculus midterm 1 practice problems: Lines
1. Find the equation of the line with slope 1/3 through the point (6, 2/3).
2. Find the equation of the line through the points (4, 8) and (3, 6).
3. Find the equation of the line with slope 14 and y -interce
1.) Determine the center and the radius for the circle (x 3)2 + (y 1)2 = 25. Also, nd
the y-coordinates of the points (if any) where the circle intersects the y-axis.
2.) Consider the following circle (x 4)2 + (y 1)2 = 9. Solve
1.) Use the horizontal line test to determine whether f (x) = x3 is one-to-one. Note: Since
the function is one-to-one, then it has an inverse.
For the Problems 2-4, show that the function is one-to-one by using the denition (i.
1.) Let C(x) = (1 + x2 )3 . Find functions f and g so that C(x) = (f g) is true for all
values of x.
2.) Express the following function G(x) as a composition of two simpler functions
(1 + x4 )
one of which is
f (x) =
NOTE: For the problems 1 and 2, you are constructing dierence quotients, which
is the slope of the secant line (a line that joins two points on a given curve y = f (x)
between two arbitrary points (x, f (x) and (x, f (x + h). Th
NOTE: For the following problems, you are building secant lines (a line that joins two
points on a given curve, which is indicated at the end of each problem). These secant lines
are the foundation of the denition of the derivat
Precalculus midterm 2 study guide
From midterm 1: study problems 2, 6, and 7.
Rational and algebraic functions
Determine the domain of an algebraic function.
Given the equation or graph of an algebraic function, identify its roots,
Precalculus midterm 3 practice problems: even and odd functions
1. Determine whether the following functions are even, odd, or neither. Justify your
answer with the technique of your choice. (If you choose to note graphical symmetry,
graphs must be relati
Precalculus midterm 3 practice problems:
square root equations
On midterm 2, few people did problem 3 correctly. I will place a similar
example on midterm 3. Please study the problems below for practice.
3 x = 3
x = 20
3. 4x + 2x + 5 = 0