# the coordinate

1. Given the points –2 and 3 on the coordinate line: a. Find the distance between them. (1 pt.) b. Find the midpoint of the line segment which connects them. (1 pt.) 2. Use interval notation to describe all values for x that satisfy -1 5 2x + 3 < 3. (3 pts.) X 3. Use interval notation to describe all values for x that satisfy < 2. (3 pts.) x-1 4. ) in the coordinate plane. 1 Find the distance between the points (-1, — -) and (1, 2 (1 pt.) 5. Sketch the following region of the xy-plane: {(x, y): x² + y2 < 4 and y < 1}. (1 pt.) 6. Find the equation of the circle that is shown below. (1 pt.) + 2 Q -3 -2 -1 7. Find the center and radius of the circle with equation x² + y2 – 4y = 0. Sketch this circle in the xy-plane. (3 pts.) 8. Find the equation of the circle that has its center at (1, 2) and that passes through the origin. (2 pts.) 9. Consider the graph of the equation y = 2x”. a. What type of symmetry, if any, does this graph have? (1 pt.) b. What are the x- and y-intercepts of the graph? (1 pt.) 10. Find the area of a square given that the length of each of its sides is 1 the value of 4 its area. (3 pts.) 11. Find a simplified form for the difference quotient of the function f(x) = 2x² – 3. (2 pts.) 12. What are the domain and range of the function whose graph is shown below? (2 pts.) Y Х 1 13. Find the domain of the function g(x) = VX+X votre (3 pts.) 14. Two people begin walking from the same point. One heads due north at 2 miles per hour, and the other heads due east at 3 miles per hour. Find a function d(t) that represents the distance between the two people as a function of the time (t hours) after they begin to walk. (3 pts.) + x 15. Determine if the function h(x) = is even, odd, or neither. (1 pt.) x
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