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