3-5 Equations, Tables, and Graphs
[Pages:15]3-5 Equations, Tables, and Graphs
Warm Up For each function, find the value of y for x = 0, x = 4, and x = ?5.
1. y = 6x ? 3
2. y = 3.8x ? 12
3. y = 1.6x + 5.9
3-5 Equations, Tables, and Graphs
Additional Example 1: Using Equations to Generate Different Representations of Data
The height h of an airplane s seconds from take-off is h = 12s. Make a table and sketch a graph of the equation.
Equation
h = 12s
An equation shows how the variables are related. Helpful Hint
The number of seconds s is the input value. The depth d is the output value.
3-5 Equations, Tables, and Graphs
Additional Example 1 Continued Table
s h 0 0 1 12 2 24 3 36
A table identifies values that make the function true.
3-5 Equations, Tables, and Graphs
Additional Example 1 Continued Graph
h 50 40 30
20
10
0 1 2 3 4 5s
A graph is a visual image of the values in the table. In this case, the graph is continuous, so draw a line through the points.
3-5 Equations, Tables, and Graphs
Check It Out: Example 1
The height h in feet of a helicopter s seconds from take-off is 15s. Make a table and sketch a graph of the function.
3-5 Equations, Tables, and Graphs
Check It Out: Example 1 Continued
s h 0 0 1 15 2 30 3 45 4 60
3-5 Equations, Tables, and Graphs
Check It Out: Example 1 Continued
h
60 45 30 15
s
0 12 3 4
Time (seconds)
Height (feet)
3-5 Equations, Tables, and Graphs
Additional Example 2: Using Tables to Generate Different Representations of Data
Use the table to make a graph and to write an equation.
x y 0 ?1 1 0 2 1 3 2
Look for a pattern in the values:
0 = 1 ? 1 1 = 2 ? 1 2 = 3 ? 1
Each value of y is the value of x minus 1.
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