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5-4 Review Notes: Writing a Function Rule5-5 Review:Direct Variation
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Example 1: Writing a Function Rule from a Table
X f(X)
1 5
2 6
3 7
4 8
What do you do to x to get f(x)?
Relate: f(x) equals x plus 4
f(x)= x + 4
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2. x y
1 1
3 9
6 36
9 81
Relate: y equals x times itself
y = x2
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3. x f(x)
1 -1
2 0
3 1
4 2
Relate: f(x) equals x minus 2
f(x)= x-2
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4. x y
1 2
2 4
3 6
4 8
Relate: y equals x times 2
y = 2x
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Example 2: Real World Problem Solving
1. A carpenter buys finishing nails by the pound. Each pound of nails costs $1.19. Write a function rule to describe this relationship.
Relate: cost equals 1.19 times nails (x)
C(x) = 1.19x
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Direct Variation
A function in the form y = kx.
The constant of variation (k) is the coefficient of x.
Step 1: Solve for y.
Step 2: Is it in y = kx form?
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Ex 1: Is the equation in direct variation form?
1.5x + 2y = 0
2.5x + 2y = 9
3.7y = 2x
4.y – 7.5x = 0
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Ex. 2: Writing an equation given a point .
1.(4, -3)
2.(-3, -6)
3.(-3, 2)
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Ex. 3: Does the table vary directly, if so write an equation in direct variation form.
X Y
-3 2.25
1 -0.75
4 -3
6 -4.5
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X Y
2 -1
4 1
6 3
9 4.5
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HW #12
Pg. 256 (1-17)
Pg. 264 (1-21 odd)