week 7 teach your lesson by Nathaniel Clark

8th grade

nathanielclarknlc — 2024-08-11 15:44:29 UTC

CA CSS math 8.F.5; Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Goal: Students can describe the relationship between two quantities on a graph

Linear vs Nonlinear.

Problem 1

nathanielclarknlc — 2024-08-11 15:50:39 UTC

Does the graph of the equation y = 4 – x increase or decrease?

It decreases because the y value decreases from left to right. X increases but that does not mean the graph increases.

Problem 2

nathanielclarknlc — 2024-08-11 15:54:32 UTC

Which of the following functions is constantly increasing?

y = x² + 3
y = -2x
y = x – 7
y = |4x|

It is y= x-7

This is the only linear function that has a positive slope, so will constantly increase.

Problem 3

nathanielclarknlc — 2024-08-11 15:57:11 UTC

Which of the following functions is constantly decreasing?

y = x
y = ½x³
x + y = 3
y = -x² – 1

It is x+y=3

This one has a negative slope when written and is the only one with a constant negative slope.

Problem 4

nathanielclarknlc — 2024-08-11 15:59:21 UTC

Which of the following has no turning points?

Linear
Quadratic
Absolute value
None of the above

Linear is the answer.

It is the only one that doesn't have any turns or U shapes like Quadratics.

Problem 5

nathanielclarknlc — 2024-08-11 16:02:19 UTC

Which of the following sets of points does not form a function?

(0, 0), (0, 1), (0, 2)
(0, 0), (1, 0), (2, 0)
(0, 3), (1, 4), (2, 5)
(1, 1), (2, 4), (3, 9)

Answer:(0, 0), (0, 1), (0, 2)

This is because the X value stays the same meaning the y value ends up having the same y value and cannnot form a function.

References

nathanielclarknlc — 2024-08-11 16:04:27 UTC

Common Core Standards : CCSS.Math.Content.8.F.B.5. (n.d.). https://www.shmoop.com/common-core-standards/ccss-8-f-5.html