Draw the graph of the following linear function and give

Question

1. Draw the graph of the following linear function and give the domain and range.

f(x) = -½x + 5

2. Solve the following equation.

|x| = 3.

3. Give the inequality whose graph is shown below.

4. Evaluate the following expression when x = 3 and y = 2.

2xy - x²y

5. Completely factor the following expression.

16x⁴ - 81y⁴

6. Perform the following division.

(y² + 10y + 21) ÷ (y + 7)

7. Solve the inequality below and write the solutions in interval notation.

|2m + 3| < 13

8. Write the numeral 0.0685 in scientific notation.

9. Given f(x) = -6x - 1, find f(2).

10. Write the equation of the line with a slope of 2 and passing through the point (-5, 3).

11. Simplify the following expression completely:

(ab^-3/3a^-2b²)²

12. Solve the system of equations given below.

x + 3z = 12

-x - 2y + z = 10

3x + 5y + 2z = -7

13. Do the following two lines intersect? Answer yes or no, together with the point of intersection; if any

5x - 8y = -5

-x - 1.6y= 14

14. Compute the determinant.

4        0      -1

3        6      -2

-2       5      1

15. Compute the distance between the two points (1- √2, -1) and (2 +√2, 4).

16. Rationalize the denominator of (2√7)/(x+√7).

17. At what x values does the parabola y = x²- 5x + 4 intersect the x axis?

18. The surface area (A) of a sphere with radius (r) is given by A = 4πr². Solve this formula for r.