Increase of Function Range & Regions in Algebra Problems

Hi,

I need step by step solutions for all the questions in the attached assignment.

Thanks 🙂

Properties of Functions
For each graph, determine the following properties.
(a) Find the domain of the function Express your answer in interval notation.
(b) Find the range of the function Express your answer in interval notation.
(c) Locate any local maximum or minimum values. (You do not need to include the endpoints)
(d) Estimate the x and y coordinates for the absolute maximum value.
(e) Estimate the x and y coordinates for the absolute minimum value.
(f) Determine the regions where the function is increasing. Give your answer in interval notation.
(e) Determine the regions where the function is decreasing. Give your answer in interval notation.
(h) is the function even, odd or neither?
11.
12.
13.
5
4
10
8
61
4
2
4
3
0104
84
6+
44
2+
x
+X
4 6 8 10
2
34
5
-10-8-6-4-
4 6 8 10
2
-10-8-6-4-2
-2
-4
-6
-8
-101
-6+
-3+
–
de
-10-1
14. Given the function f(x) = Vx+2:
(a) Evaluate f(7)
(b) Solve f(x) = 4.
15. For the following exercises, write a formula for the function obtained when the graph is shifted as described.
(a) f(x) = (xis shifted down 3 units and to the right 1 unit.
(b) f(x) = is shifted down 4 units and to the right 3 units.
16. Suppose the function shown in the graph to the right is f(x) = 2*
Sketch each of the following transformations on the graph.
(a) g(x) = 22 +1
(b) h(x) = 22 – 3
(c) w(2) = 24-1
3
2
X
Algebra Skills
1.
Solve for x, show your work.
2.
Simplify these rational expressions, show your work.
(a)
(a)
(x + 1)? – 7 = 9.
(b)
(3.-7)(4x – 5) + x = 5.
1 – 12
(b)
(c)
= 2
3
16
22+72-78
20+1
3+13
1
(d)
2 7
+
Зr 1 –
3.
Assume that student performance on an exam is directly proportional to study time.
If a student can score 70 points on an exam with 5 hours of study, what score would
the student get with 7 hours of study?
V: +3-r= -3.
) (f)
4.
15x – 2 = 8
Jack is an avid runner. He runs up a steep mountain trail 4 miles long and then
returns on the same trail. Uphill he goes one mile per hour faster than half his
downhill rate. If the round trip time is one hour and forty minutes, then what is
Jack’s downhill rate?
(8)
– 2x + 71 > 10.
()
(h)
5. A coolant reservoir contains 9 liters of a 20 percent antifreeze solution. How many
liters of the antifreeze must be drained and replaced with pure water in order to
achieve a 15 percent antifreeze solution?
6. Use interval notation to express the numbers shown
by the lines, arrow, circles and dots shown on the
number line.
(a)
2
(b)
9. A pencil is thrown off a cliff and travels downwards under the force
of gravity on the Earth. d = 3t+16t, where t is measured in
seconds. How long will it take for the object to travel 84 ft?
4
(c)
2
7. Solve for x, express the solution using the number line
(a)-5-+
(b) |x-11 > 2
(c) < +31 > 5
10. A farmer wants to enclose a rectangular space for a new garden. She
has purchased 80 feet of wire fencing to enclose 3 sides, and will put
the 4th side against the backyard fence. Find a formula for the area
enclosed by the fence if the sides of fencing perpendicular to the
existing fence have length L.
Hint use the formula for the perimeter of the fence and the area of the
garden to write two equations in terms of the length and width.
8. Simplify these expressions involving complex numbers:
(a) (5 – 21) (31)
(b) (3 +41) (3 – 41)
(c) ✓-9+37-16
(d) 18
24.
For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear
equation that models the data.
2
6
8
(a)
16
36
56
(b)
5
10
20
25
13
28
58
73
(c)
I
0
5
10
15
5
-10
-25
-40
25.
For each pair of points:
(1) Find the distance between the points using the distance formula/.
(ii) Find the midpoint
(iii) Determine the line which connects the points, write it in standard form
(a) (-1,4) and (5,2)
(b) (8,-2) and (4,6)
7
17. For the graph shown on the right:
(a) Estimate the average rate of change from x = 1 to 2 = 4.
(b) Estimate the average rate of change from a = 2 to 3 = 5.
6
5
4.
N w V
3
21
18. Let f(x) = (1 – 1). Is f(x) even, odd or neither?
1
0
1
2
3
4
5
6
7
8
19. Explain how to get the graph of -f(x – 5) + 2 from the graph of f(x).
20. Let f(x) – 4-T+2 and g(2) = 4 –
(a)
Find the domains of both f(x) and g(). Determine whether f(t) is even, odd, or
neither. Do the same for g(x).
(b)
Describe f(x) as a reflection followed by horizontal and vertical shifts.
(c) Evaluate (fog)(x).
Linear Functions
21. Find the slope-intercept form of the equation of the line that has these properties:
(a). An x-intercept (-2, 0) and y-intercept of (0,4)
(b). A y-intercept of (0,7) and slope ->
22.
Write an equation for these lines.
(a)
(b)
6
5
(c)
5-
5
4
4
3
2
2
1
3
21
1
432
32
o
1
2 3 4
2
-1
0
1
1
13
3
4
-4
“5
5
23. Find the slope-intercept form of the equation of the line that passes through (7,2)
and perpendicular to 14.0 – 2y = 1.