ST 552

Calculus on a Computer

Assignment 1 Review of Algebra & Trigonometry

1. Sketch the set of points described by |3x-5| < 2.

2. Use absolute values to describe the set -1/2 < x<3 with a single inequality.

3. Find the equation of the circle that goes through (1,2), (2,0), and (4,1). What are the center and the radius?

4. Give equations (in slope-intercept form) and graph the following lines:

a. The line through (1,-2) with slope 2.

b. The line through (2,3) and (4,1)

c. The line through (2,-3), perpendicular to y = -2x-1

d. The line parallel to y=1/2 x+3, through (1,1)

5. Let f(x) = _. Use MAPLE to plot the following, and describe the changes.

a. f(x+2)

b. f(3x)-2

c. 2*f(2x)

d. f((x+1)/2)

6. Show on a unit circle the angles with:

a. sin(x) = .3

b. cos(x) = -.75

c. tan(x)=2

7. Which of the following define y as a function of x? Explain.

a.

b.

c. y=5

d.

8. Let f(x) = cos(x), and g(x)= _. What is f(g(x))? g(f(x))? Are they the same? Use MAPLE to plot them.

9. Which of the following are polynomials? Explain.

a.

b.

c.

d.

1. Plot the functions in exercise 9.