The graph represents function that gives the height in inches of a bamboo plant months after it has been planted.
What does this statement mean?
What is the value of ?
What is if ?
What is the value of ?
How many inches does the plant grow each month? How can you see this on the graph?
13.2
Activity
A Growing Account Balance
Standards Alignment
Building On
8.F.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The balance in a savings account is defined by the function . This graph represents the function.
Find the values:
Calculate .
You should have gotten the same value twice. What does this value have to do with this situation?
13.3
Activity
The Temperature Outside
Standards Alignment
Building On
8.F.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Here are a graph and a table that represent the same function. The function relates the hour of day to the outside air temperature in degrees Fahrenheit at a specific location.
0
48
6
57
1
50
7
56
2
55
8
55
3
53
9
50
4
51.5
10
52
5
52.5
Scatterplot. Horizontal axis, time in hours. vertical axis, temperature in degrees fahrenheit. Points plotted at 0 comma 48, 1 comma 50, 2 comma 55, 3 comma 53, 4 comma 51 point 5, 5 comma 52 point 5, 6 comma 57, 7 comma 56, 8 comma 55, 9 comma 50, and 10 comma 52.
Match each expression to a value. Then explain what the expression means in this situation.
4
-2
47
-1.4
55
14
-8
38
-10
52
Glossary
None
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Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.