# 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

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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 â‰ 4, not a solution

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

(-4, 0): x - y = -4 - 0 = - 4 â‰ 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 ï‚£ -2

The line y = -2 is the horizontal line passing through (0, -2). y ï‚£ -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

A) x =

B) x =

C) x = 1

D) x = -1

7. Solve. x2 + 9 = 34

Take the square root on both sides:

A)

B)

C) Â±5

D)

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?

The slope is then

A) 7.60

B) 0.13

C) 1.47

D) 6.48

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

In the standard slope- intercept form y = mx + b, the slope is m and b is y-intercept.

So m = 5 and b = -3

The line equation is y = 5x - 3

A) y = -3x + 5

B) -3x + 5y = 0

C) y = 5x - 3

D) 5y = -3

10. Match the graph with one of the equations.

Obviously, the slope of the line is positive. so only B and D are possible equations.

The y-intercept is (0, 1). The line also passes through point (1, 4). So the slope is

Therefore, the equation is y = 3x + 1

A)

B)

C) y = -3x + 1

D) y = 3x + 1

11. Simplify.

=

A)

B)

C)

D)

12. Find the y-intercept.

-x + 2y = -10

For y-intercept, x = 0, substituting 0 for x to the equation to solve for y:

0 + 2y = -10, then y = -5.

So y-intercept is (0, -5).

A) (10, 0)

B) (0, -5)

C) (-5, 0)

D) (0, 10)

13. Solve the system by addition or substitution.

3x + 5y = 2 (1)

2x + 5y = -2 (2)

By addition, (1) - (2):

Substituting 4 for x to equation (1) to find y:

So the solution to the system is .

14. Determine whether is rational or irrational.

Therefore, it is a rational.

A) Rational

B) Irrational

15. Find the x-intercepts.

y = x2 + 5x + 1

for x-intercepts, y = 0, solving the quadratic equation by quadratic formula:

A)

B)

C)

D)

16. Determine which two equations represent parallel lines.

When two lines are parallel, their slopes are equal.

In the standard slope-intercept form y = mx + b, m is the slope.

Thus, (c) and (d) are parallel because both slopes are equal to 9.

(a) y = x + 1

(b) y = x - 4

(c) y = 9x + 6 (d) y = 9x - 1

A) (a) and (b)

B) (b) and (c)

C) (a) and (d)

D) (c) and (d)

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

Take the square root:

A)

B)

C)

D)

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

For a slope of 0, the line is horizontal. So all points on the line have the same y-coordinates.

The line equation is then y = -2.

Or you can use y = mx + b to find the equation:

The slope m = 0, then y = b

Since the line passes through (-6, -2), b = -2.

A) x = -6

B) x = -2

C) y = -6

D) y = -2

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%?

Assume he invested x dollars at 18%, then (28000 - x) was invested at 9%.

The interest from 18% investment is interest = principle * rate = x * 18% = 0.18x.

The interest from 9% investment is 0.09(28000 - x).

So the total interest is

0.18x + 0.09(28000 - x) = 3240

0.18x + 2520 - 0.09x = 3240

0.09x = 720

x = 8000

A) $20,000

B) $9,000

C) $8,000

D) $7,000

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

3x + 4y ï‚£ 12

x + 3y ï‚£ 6

x ï‚³ 0

y ï‚³ 0

First draw the two boundary lines and .

Then using "test a point" method to find which side of the line satisfies the inequality.

For , using the origin (0, 0) as the test point,

3x + 4y = 0 < 12, so (0, 0) satisfy the inequality.

Thus, the solution to should be at the same side of the line as the origin.

Repeat the same procedure for , we also find the solution to is at the same side of the line as the origin.

Thirdly, and limit the inequalities in the first quadrant.

Finally, find the common area of all inequalities and shade it as the solution.

A)

B)

C)

D)

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

Apply Pythagorean theorem:

Take the square root:

Only the positive number makes sense. So x is 24.

A) 18 ft

B) 24 ft

C) 10 ft

D) 68 ft

22. Simplify.

A)

B)

C)

D)

23. Is the following trinomial a perfect square?

x2 - 6x - 9

The perfect square formula is

No matter a is positive or negative, is always positive.

In the trinomial x2 - 6x - 9, in a2 position we have -9, which is negative. so it is not a perfect square.

You can verify by yourself that x2 - 6x + 9 is a perfect square.

A) Yes

B) No

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