Access over 20 million homework documents through the notebank

Get on-demand Q&A homework help from verified tutors

Read 1000s of rich book guides covering popular titles

Anonymous

I did an assignment, got 79/100 and professor gave feedback. I need someone to fix it. I am attaching the original instructions, the work I did and the feedback I received.

Assignment #1
MAC 1140 – Spring 2020 – Due: March 27, 2020
1. Determine whether each of the following relationships is a function and give the domain and range
for each relation.
Relation
Function?
Yes
No
Domain
Range
(a) {(1,4), (4,4), (1,3), (6,3)}
(b) {(1,3), (2,5), (5,6), (3,7)}
(c) {(−3, −3), (−1, −1), (7,0)}
2. Determine whether each of the following equations defines 𝑦 as a function of 𝑥.
Equation
Function?
Yes
No
Explain your rationale
(a) 𝑥 + 𝑦 = −3
(b) 𝑥 + 𝑦 2 = −3
(c) |𝑥| + 𝑦 = 0
(d) 𝑥 2 + 𝑦 2 = 1
1
3. You are given the following function. Find:
(a) The domain of the function: ___________
(b) The range of the function: ___________
(c) The 𝑥-intercepts (approximate, as necessary): _____________________
(d) The 𝑦-intercept: ___________
(e) Intervals on which 𝑓(𝑥) is decreasing: _________________________________
(f) Intervals on which 𝑓(𝑥) is increasing: _________________________________
(g) Intervals on which 𝑓(𝑥) is constant (if any): ____________________________
(h) The values of 𝑥 where 𝑓(𝑥) = 3 (approximate, as necessary): _______________
(i) The relative maxima of the function: (𝑥, 𝑦) = ____________________________
(j) The relative minima of the function: (𝑥, 𝑦) = ____________________________
(k) The absolute maximum of the function: (𝑥, 𝑦) = ________
(l) The absolute minimum of the function: (𝑥, 𝑦) = ________
(m) Is the function even odd, or neither? ______________
2
4. Sketch the graph of 𝑓(𝑥) = 𝑥 2 − 4𝑥 and identify all the relative extrema and absolute extrema of
the function on each of the following intervals.
(a) (−∞, +∞)
(b) [−1,4]
(c) [1,3]
(d) [3,5]
(e) (−1,5]
3
5. Find the difference quotient for the following functions:
(a) 𝑓(𝑥) = 3
(b) 𝑓(𝑥) = −2𝑥
(c) 𝑓(𝑥) = 4𝑥 2
(d) 𝑓(𝑥) = 5𝑥 2 + 2𝑥 − 4
4
6. For each case below, use the conditions to write an equation for each line in point-slope form and
slope-intercept form.
(a) slope = −2, passing through (3,5)
(b) passing through (0, −2), with 𝑥-intercept = −1
(c) passing through (0, −2) and (3,5)
(d) 𝑥-intercept = 2, with 𝑦-intercept = −3
(e) passing through (1,1), parallel to the line 𝑦 = −3𝑥 + 2
1
(f) passing through (0,0), perpendicular to the line 𝑦 = 3 𝑥 − 2
5
7. (a) Find the distance between the points (2, −3) and (5,4). If necessary, express your answer in
simplified radical form and then round to two decimal points.
(b) Find the midpoint of the line segment with endpoints at (2, −3) and (5,4).
(c) Write the standard form of the equation of the circle with radius 𝑟 = 2 and center (−1,3).
(d) Find the center and radius of the circle given by 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 − 4 = 0.
6
8. You are given the quadratic function 𝑓(𝑥) = −𝑥 2 − 2𝑥 + 3.
(a) Without graphing, determine if the function has a minimum or maximum and explain your
reasoning.
(b) The coordinates of the vertex are:
(c) The intercepts are:
(d) The equation of the parabola’s axis of symmetry is:
(e) Graph the function.
(f) The domain of the function is:
(g) The range of the function is:
7
...

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors