Section 5.7 PartB Sketching Graphssoln.notebook
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Sec 5.7: Interpreting Graphs of Linear Functions (Continued)
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Summary From Last Class
• The xintercept is where the graph cross the _______________ axis.• This point is always: _____________
• The yintercept is where the graph cross the _______________ axis.• This point is always: _______________
New
We can use this idea to determine the x and y intercepts without graphing!
We can determine the x‐intercept by substituting y = 0, or f(x) = 0 into the function and solving for x.
We can determine the y‐intercept by substituting x = 0, or f(0) into the function and solving for y.
Section 5.7 PartB Sketching Graphssoln.notebook
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a) What is the x‐intercept of the function, f(x) = x – 3? Write it as a point.
b) What is the y‐intercept of the function, f(x) = x – 3? Write it as a point.
Section 5.7 PartB Sketching Graphssoln.notebook
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c) Plot the graph f(x)=x3.
NOTE: To graph a line you ONLY need two points!
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To graph a linear function you will need of the following
1) the vertical (y) intercept and horizontal (x) intercept. (Just completed this method on previous page.)
2) any two points
3) the vertical (y) intercept and the rate of change (slope)
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1. Sketch the function using the two intercept method.
Examples:
f(x) = ‐2x + 4
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2. Sketch g(x) = 2x 6 using any two points.
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3. Sketch using the vertical intercept and the rate of change (slope)
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4. Sketch using the vertical intercept and the rate of change (slope)
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5. Graph the line that has a vertical intercept of 6 and a rate of change of – 2.
Note:
Any slanted or oblique line will have two intercepts, the x‐intercept and the y‐intercept.
What type of line will have only one intercept?
• Any vertical line or horizontal line that is not an axis, will only have one intercept.
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7. Graph the line x = ‐ 4.
Crosses the x‐axis in one place.It has an x‐intercept (‐4,0).
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8. Graph the line y = 2.
Crosses the y‐axis in one place.It has an y‐intercept (0,2).
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What type of line will have an infinite number of intercepts?
• Any line that lies on the x or y‐ axis, will only have an infinite number of intercepts.
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