10 College Algebra Problems
Show your work on all the problems.
1. Find the midpoint of the segment with endpoints (5, –2) and (7, 4).
2. The point (4, –1) is on a circle with center (7, 3). Find the length of the radius of the circle.
3. Simplify:
8
5
-
3
-4
y
x
4
y
x
32
-
a. Find the slope-intercept equation for a line with slope 5 and which passes through the point (1, –2).
b. Find the slope of the line through the points (8, 1) and (7, 3).
5. Find the domain of the functions:
a.
2
x
3
f(x)
+
=
b.
5
6x
-
x
1
f(x)
2
+
=
6. Determine whether the graph of y = 3 + x2 is symmetric with respect to the x-axis, the y-axis, or the origin.
7. A salesperson earns a base salary of $2,000 per month and a commission of 5% on the amount of sales made. If the salesperson has a paycheck of $3,006 for one month, what was the amount of sales for the month?
8. For x values in what interval (s) is the function increasing?
9.
a. Given f (x) = 4/x2 and g(x) = 3 – 2x, find the composite function (f o g)(x) and simplify.
b. Write the equation for a function that has a graph with the given characteristics.
The shape of y = |x| but stretched vertically by a factor of 2 and shifted right 3 units.
10.
a. Solve for n: 2(n - 1) = 3(n + 5)
b. Find the zero of the function f(x) = 8 – 2x