# Functions and equations

I need help answering these practice questions. I have attached the questions that I need help with. Please explain your answers in detail.

1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7)are solutions for the equation x - y = 4?

2. Given f(x) = 5x - 1, find f(a + 3).

3. Solve by completing the square. x2 = 5x + 2

4. Find the slope of the line passing through the points (-10, 4) and (-4, -1).

5. Graph the inequality.

6. Find the axis of symmetry.

7. Solve. x2 + 9 = 34

8. A roof rises 2.75 ft over a horizontal distance of 20.91 ft. What is the slope of the roof to the nearest hundredth?

9. Write the equation of the line with slope 5 and y-intercept (0, -3).

10. Match the graph with one of the equations.

11. Simplify.

12. Find the y-intercept.

13. Solve the system by addition or substitution.

14. Determine whether is rational or irrational.

15. Find the x-intercepts.

16. Determine which two equations represent parallel lines.

17. Solve. 5(x - 2)2 = 3

18. Write the equation of the line that passes through point (-6, -2) with a slope of 0.

19. Lane invested $28,000, part at 18% and part at 9%. If the total interest at the end of the year is $3,240, how much did she invest at 18%?

20. Solve the following system of linear inequalities by graphing.

21. Find the length x. Express your answer in simplified radical form.

22. Simplify.

23. Is the following trinomial a perfect square? x2 - 6x - 9

#### Solution Preview

Please see the attached file for detailed solution.

1. Which of the ordered pairs

(3, 1), (0, -4), (-4, 0), (-3, -7)

are solutions for the equation x - y = 4?

Substituting each of the ordered pair to the equation to check:

(3, 1): it means x = 3 and y = 1, so x - y = 3 - 1 = 2 ≠ 4, not a solution

(0, -4): x - y = 0 - (-4) = 4, solution

(-4, 0): x - y = -4 - 0 = - 4 ≠ 4, not solution

(-3, -7): x - y = - 3 - (-7) = 4, solution

A) (0, -4), (-4, 0), and (-3, -7)

B) (-4, 0) and (-3, -7)

C) (0, -4) and (-3, -7)

D) (3, 1) and (-4, 0)

2. Given f(x) = 5x - 1, find f(a + 3).

Treat a + 3 as one variable and replace x with a + 3 in the function:

f(a + 3) = 5(a + 3) - 1 = 5a + 15 - 1 = 5a + 14

A) 5a + 14

B) 5a + 2

C) a + 7

D) a + 14

3. Solve by completing the square.

x2 = 5x + 2

Then take the square root on both sides

A)

B)

C)

D)

4.

Find the slope of the line passing through the points A(-10, 4) and B(-4, -1).

The slope is defined as the rate of change in y in terms of x:

So

A)

B)

C)

D)

5. Graph the inequality.

y -2

The line y = -2 is the horizontal line passing through (0, -2). y -2 should be the half-plane below the line y = - 2. The boundary line y = -2 should be solid since y = - 2 is part of the inequality.

A)

B)

C)

D)

6. Find the axis of symmetry.

y = x2 - x + 5

By completing the squares:

Thus, the axis of symmetry is ...

#### Solution Summary

This provides several examples of working with functions, equations, and graphing, including slope, inequalities, symmetry, and determining solutions.