Graphing Linear Functions

1
Given g(x) 2x2 1 , find g(3)
g(3)2(3)2 1
g(3)2(9)1
g(3)19
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3.3 Linear FunctionsThe student will be able to
1. identify linear functions. 2. write equations
in standard form. 3. Graph linear
functions. Indicators
Designed by Skip Tyler, Varina High School
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Vocabularies

• A linear equation is the equation of a line.
• An x-intercept is a point on the graph where y is
  zero. In other words, an x-intercept is a point
  in the equation where the y-value is zero.
• A y-intercept is a point on the graph where x is
  zero. In other words, a y-intercept is a point in
  the equation where the x-value is zero.
• Values of x for which f(x)0 are called zeros.
  For a linear function, the zero is its
  x-intercept.

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Standard FormAx By CA, B, and C have to be
integers

• An equation is LINEAR (the graph is a straight
  line) if it can be written in standard form.
• This form is useful for graphing (later on).

5
Determine whether each equation is a linear
equation.

• 4x 7 2y
• Can you write this in the form
• Ax By C?
• 4x - 2y 7
• A 4, B -2, C 7
• This is linear!

6
Determine whether each equation is a linear
equation.

• 2) 2x2 - y 7
• Can you write it in standard form?
• NO - it has an exponent!
• Not linear
• 3) x 12
• x 0y 12
• A 1, B 0, C 12
• Linear

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Heres the cheat sheet! An equation that is
linear does NOT contain the following

• Variables in the denominator
• Variables with exponents
• Variables multiplied with other variables.
• xy 12

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Is this equation linear?

1. Yes
2. No

Standard Form x 4y 3
9
Is this equation linear?

1. Yes
2. No

Exponents are not allowed!
10
Is this equation linear?y -3

1. Yes
2. No

Standard Form 0x y -3
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• Review of the definition.
• An x-intercept is a point on the graph where y is
  zero. In other words, an x-intercept is a point
  in the equation where the y-value is zero.
• A y-intercept is a point on the graph where x is
  zero. In other words, a y-intercept is a point in
  the equation where the x-value is zero.
• Values of x for which f(x)0 are called zeros.
  For a linear function, the zero is its
  x-intercept.

12
Determine the x-intercept, y-intercept, and zero
of the linear equation y10x-1.
x-intercept
y-intercept

• Set y0

• Set x0

• Solve for x

• Solve for y

010x-1
y10(0)-1
1 1
110x
y-1
x1/10
13
Determine the x-intercept, y-intercept, and zero
of the linear equation y10x-1.
x-intercept
y-intercept
14
Find the x-intercept, y-intercept, and zero for
the graph of the line.
Solution The x-intercept of this graph is 4. The
coordinates of the point at the x-intercept is
(4, 0). The y-intercept of this graph is 2. The
coordinates of the point at the y-intercept is
(0, 2).
15
Find the x-intercept, y-intercept, and zero for
the graph of the line.
x-intercept -3 y-intercept 3 zero -3
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Graph an equation by making a table
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Graphing Steps

1. Isolate the variable (solve for y).
2. Make a t-table. If the domain is not given, pick
   your own values.
3. Plot the points on a graph.
4. Connect the points.

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1) Review Solve for y 2x
y 4

1. Draw the river
2. Subtract 2x from both sides

- 2x - 2x
y -2x 4
2) Solve for y 4x 2y -6
- 4x - 4x 2y -4x
- 6 2 2
y -2x - 3

1. Subtract 4x
2. Simplify
3. Divide both sides by 2
4. Simplify

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3) Solve for y x - 3y 6
- x - x -3y -x 6
-3 -3

1. Subtract x
2. Simplify
3. Divide both sides by -3
4. Simplify

or
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Review Make a t-tableIf f(x) 2x 4, complete
a table using the domain -2, -1, 0, 1, 2.
x
f(x)
ordered pair
-2

• 2(-2) 4 0 (-2, 0)
• 2(-1) 4 2 (-1, 2)
• 2(0) 4 4 (0, 4)
• 2(1) 4 6 (1, 6)
• 2(2) 4 8 (2, 8)

-1
0
1
2
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Given the domain -2, -1, 0, 1, 2, graph 3x
y 6

• Solve for y 3x y 6
• Subtract 3x

- 3x - 3x
y -3x 6
2. Make a table
ordered pair
x
-3x 6

• -3(-2) 6 12 (-2, 12)
• -3(-1) 6 9 (-1, 9)
• -3(0) 6 6 (0, 6)
• -3(1) 6 3 (1, 3)
• -3(2) 6 0 (2, 0)

-2 -1 0 1 2
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1. Given the domain -2, -1, 0, 1, 2, graph 3x
   y 6

1. Plot the points(-2,12), (-1,9), (0,6), (1,3),
   (2,0)
2. Connect the points.

• Bonus questions!
• What is the x-intercept?
• (2, 0)
• What is the y-intercept?
• (0, 6)
• Does the line increase or decrease?
• Decrease

23

1. Given the domain -2, -1, 0, 1, 2, graph 4x
   2y 6

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Which is the graph of y x 4?

1. .
2. .
3. .
4. .

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• Assignment ????