5-4 Review Notes: Writing a Function Rule5-5 Review:Direct Variation

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

2. x y

1 1

3 9

6 36

9 81

Relate: y equals x times itself

y = x2

3. x f(x)

1 -1

2 0

3 1

4 2

Relate: f(x) equals x minus 2

f(x)= x-2

4. x y

1 2

2 4

3 6

4 8

Relate: y equals x times 2

y = 2x

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

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?

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

Ex. 2: Writing an equation given a point .

1.(4, -3)

2.(-3, -6)

3.(-3, 2)

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

X Y

2 -1

4 1

6 3

9 4.5

HW #12

Pg. 256 (1-17)

Pg. 264 (1-21 odd)