2. how would you translate the graph of y = -x? to produce the graph of y =)?
a. translate the graph of y = -x' up 6 units
b. none of these
c. translate the graph of y = -x? down 6 units
d. translate the graph of y = -x right 6 units
e. translate the graph of y = -x? left 6 units

The purpose of this warm-up is for students to reason about the values we can assign graphs based on which feature of the graph, such as slope and -intercept, the viewer focuses on. Since there are no numbers on the graph, it is important for students to explain how they know the sign of the slope and -intercept based on the position of the graph.

Launch

Display the three graphs for all to see. Tell students that all three graphs have the same scale. Give students 1–2 minutes of quiet work time, followed by a whole-class discussion.

Student Facing

Diego said that these graphs are ordered from smallest to largest. Mai said they are ordered from largest to smallest. But these are graphs, not numbers! What do you think Diego and Mai are thinking?

Three graphs. First line crosses the y axis above the origin, slopes down & right. Second, a horizontal line lies above the x-axis. Third line crosses the y axis below the origin, slopes up & right.

Student Response

Student responses to this activity are available at one of our IM Certified Partners

Activity Synthesis

Display the three graphs for all to see. Invite students to share what they think Diego and Mai are thinking. Encourage students to reference the graphs in their explanation. Record and display their responses for all to see. Emphasize that even though there are no numbers shown, we can tell the sign of the slope and the sign of the -intercept based on the position of the line.

Step-by-step explanation:

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: