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Problem 5. Consider the function f(x) = |r + 1. (a) Does the graph of the function f have a tangent line at the point (0, 1)? If so, give the equation of the tangent line to the graph of f at this point (0, 1). If not, explain why not. (b) Does the graph of the function f have a tangent line at the point (-1,0)? If so, give the equation of the tangent line to the graph of f at this point (-1,0). If not, explain why not.

Problem 5. Consider the function f(x) = |r + 1. (a) Does the graph of the function f have a tangent line at the point (0, 1)? If so, give the equation of the tangent line to the graph of f at this point (0, 1). If not, explain why not. (b) Does the graph of the function f have a tangent line at the point (-1,0)? If so, give the equation of the tangent line to the graph of f at this point (-1,0). If not, explain why not.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
ChapterA: Appendix: Review Topics
SectionA.3: Introduction To Functions
Problem 29PS: Suppose you have a job that pays $8.50 per hour and you work anywhere from 10 to 40 hours per week....
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HOMEWORK FOR WEEK 1 TUESDAY. Problem 3. Consider the following function (DUE TUESDAY 9/7 NOON) f:(-2, 2) - R, f(z) = *+ |r+1. (a) What is the domain and codomain of f? (b) What is the image (or range) of f? Hint: Maybe try to graph f first. To handle the absolute value, remember you can rewrite the absolute (Updated September 2, 2021 at 3:11am) if w 20 -w if w <0' Instructions: Here is the first half of the homework of this week, from Tuesday's lecture. After Thursday's lecture we will have another for Thursday's material. If you are stuck on any, I will have office hours on Friday at 5pm on Zoom. Write them neatly and clearly and take a clear photo/scan of them and upload it to Canvas. Label each problem clearly so I know where to look. value function in a piecewise fashion, Ju = Problem 4. Consider the function f(x) = r + r+1. (a) Let G be the graph of f on the plane, and consider the point P = (1,3) on this graph G. Find the equation of the tangent line to the graph G at the point P using the method of limiting secant lines. (Recall how to do this, consider another point Q = (2, f(2)) on this graph and the secant line PQ, write out the slope of the secant line mpg = ., remember to factor, and let r approach the relevant value.) (b) Consider the same graph G of f on the plane again, but this time we consider the point P = (a, a? + a + 1), for some real number a. Find the equation of the tangent line to the graph G at the point P using the method of limiting secant lines. Your answer will depend on a. (Don't be scared! This time we just have some unspecified a. Consider another point Q = (x, f(x)), write out the expression of the slope mpo of the secant line PQ. Remember to factor, and then let r approach a. With the slope found, you can write out the equation of the tangent line.) (c) Using your answer from (b), is there a point on the graph G where the tangent line has a slope of –1? If so where on the graph might we find it (give the coordinate of this point)? Problem 1. Consider the following description: h:R+R, h(z) = VI+2 cos(x). Is ha correct description of a function? If not, explain what is wrong. Problem 2. A function is said to be piecewise if its rule has different descriptions on different parts of the domain. For example, f:R +R, f(x) = {1 -2 <r< 2 12 r<-2 is a piecewise function, where on the three different intervals (-00, -2).[-2, 2) and 2, o0), / have different rules. (a) Make a sketch of the graph of this function f. For parts of the function that don't terminate, indicate with an arrow on your graph. (b) What is the domain and codomain of this function f? And what is its image (or range)? (c) Does this function have a maximum? If so, indicate what is the Problem 5. Consider the function f(x) = |r + 1|. (a) Does the graph of the function f have a tangent line at the point (0, 1)? If so, give the equation of the tangent line to the graph of f at this point (0, 1). If not, explain why not. (b) Does the graph of the function f have a tangent line at the point (-1,0)? If so, give the equation of the tangent line to the graph of f at this point (-1,0). If not, explain why not. maximum value and where on the domain can we find them. (d) Does this function have a minimum? If so, indicate what is the minimum value and where on the domain can we find them. (e) On what interval is f strictly increasing? On what interval is f strictly decreasing?
Transcribed Image Text:HOMEWORK FOR WEEK 1 TUESDAY. Problem 3. Consider the following function (DUE TUESDAY 9/7 NOON) f:(-2, 2) - R, f(z) = *+ |r+1. (a) What is the domain and codomain of f? (b) What is the image (or range) of f? Hint: Maybe try to graph f first. To handle the absolute value, remember you can rewrite the absolute (Updated September 2, 2021 at 3:11am) if w 20 -w if w <0' Instructions: Here is the first half of the homework of this week, from Tuesday's lecture. After Thursday's lecture we will have another for Thursday's material. If you are stuck on any, I will have office hours on Friday at 5pm on Zoom. Write them neatly and clearly and take a clear photo/scan of them and upload it to Canvas. Label each problem clearly so I know where to look. value function in a piecewise fashion, Ju = Problem 4. Consider the function f(x) = r + r+1. (a) Let G be the graph of f on the plane, and consider the point P = (1,3) on this graph G. Find the equation of the tangent line to the graph G at the point P using the method of limiting secant lines. (Recall how to do this, consider another point Q = (2, f(2)) on this graph and the secant line PQ, write out the slope of the secant line mpg = ., remember to factor, and let r approach the relevant value.) (b) Consider the same graph G of f on the plane again, but this time we consider the point P = (a, a? + a + 1), for some real number a. Find the equation of the tangent line to the graph G at the point P using the method of limiting secant lines. Your answer will depend on a. (Don't be scared! This time we just have some unspecified a. Consider another point Q = (x, f(x)), write out the expression of the slope mpo of the secant line PQ. Remember to factor, and then let r approach a. With the slope found, you can write out the equation of the tangent line.) (c) Using your answer from (b), is there a point on the graph G where the tangent line has a slope of –1? If so where on the graph might we find it (give the coordinate of this point)? Problem 1. Consider the following description: h:R+R, h(z) = VI+2 cos(x). Is ha correct description of a function? If not, explain what is wrong. Problem 2. A function is said to be piecewise if its rule has different descriptions on different parts of the domain. For example, f:R +R, f(x) = {1 -2 <r< 2 12 r<-2 is a piecewise function, where on the three different intervals (-00, -2).[-2, 2) and 2, o0), / have different rules. (a) Make a sketch of the graph of this function f. For parts of the function that don't terminate, indicate with an arrow on your graph. (b) What is the domain and codomain of this function f? And what is its image (or range)? (c) Does this function have a maximum? If so, indicate what is the Problem 5. Consider the function f(x) = |r + 1|. (a) Does the graph of the function f have a tangent line at the point (0, 1)? If so, give the equation of the tangent line to the graph of f at this point (0, 1). If not, explain why not. (b) Does the graph of the function f have a tangent line at the point (-1,0)? If so, give the equation of the tangent line to the graph of f at this point (-1,0). If not, explain why not. maximum value and where on the domain can we find them. (d) Does this function have a minimum? If so, indicate what is the minimum value and where on the domain can we find them. (e) On what interval is f strictly increasing? On what interval is f strictly decreasing?
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