Graphs of Absolute Value Functions and lines
Exploring the intersection of an absolute values graph and a line parallel to the x-axis. Write your findings for questions in task 2 in the space provided below.
Change the value of the constant in the equation of the line in the form of y=c. (You must choose at least three different values for 'c'). For every new value of the constant you choose determine; 1. Give the coordinates of the vertex (critical point) of the absolute value graph. 2. How many times does the line y=c intersect the absolute value graph ? 3. Can be solved algebraically for your chosen value of 'c'? Are these solutions which you have determined algebraically, represented on the graph? If so, where are the solutions found on the graph?
Exploring the intersection of an absolute values graph and a line parallel to the y-axis. Write your findings for questions in task 3 in the space provided below.
Change the value of the constant in the equation of the line in the form of x=a. (You must choose at least three different values for 'a'). For every new value of the constant you choose determine; 1. How many times does the line x=a intersect the absolute value graph ? 2.Can be solved algebraically for your chosen value of 'a'? Are these solutions which you have determined algebraically, represented on the graph? If so, where are the solutions found on the graph?
Exploring the intersection of an absolute values graph and a line in the form of y=mx+c. Write your findings for questions in task 4 in the space provided below.
Change the values of the gradient and the constant in the equation of the line in the form of . (You must choose at least three different linear equations in the form of ).For every new value of the gradient and constant you choose determine; 1. How many times does the line intersect the absolute value graph ? 2.Can be solved algebraically for your chosen value of the constant and the gradient? Are these solutions which you have determined algebraically, represented on the graph? If so, where are the solutions found on the graph?
Exploring the intersection of a transformed absolute values graph and a line in the form of y=c. Write your findings for the questions in task 5 in the space provided below.
Write an equation for the absolute function in the form of . Change the values of in the equation of absolute value function and the constant in the equation of the line in the form of . (You must choose at least three different linear equations in the form of and three absolute functions in the form of ).For every new value of and constant you choose determine; 1. Give the coordinates of the vertex (critical point) of the absolute value graph you have chosen in the form of . 2. How many times does the line intersect the absolute value graph ? 3. Can be solved algebraically for your chosen value of the constant and the gradient? Are these solutions which you have determined algebraically, represented on the graph? If so, where are the solutions found on the graph? .
Exploring the intersection of a transformed absolute values graph and a line in the form of y=c. Write your findings for the questions in task 6 in the space provided below.
Write an equation for the absolute function in the form of . Change the value of the constant in the equation of the line in the form of . (You must choose at least three different linear equations in the form of and three absolute functions in the form of ). For every new value of the constant and the values you choose determine; 1. Give the coordinates of the vertex (critical point) of the absolute value graph you have chosen in the form of . 2. How many times does the line intersect the absolute value graph ? 3. Can be solved algebraically for your chosen value of the constant and the gradient? Are these solutions which you have determined algebraically, represented on the graph? If so, where are the solutions found on the graph?