Functions and rules

Write the rule a situation follows, say what each number in it stands for, read a shift or a stretch off it, and tell parallel from perpendicular — one linear rule from four sides.

4 sheets · 32 questions · one answer key · 5 pages

Recommended for grades 8–10

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Write the rule Sheet 1 of 4

Write the rule from a situationGrowing and shrinking

Name: Date:

Write each story as y = mx + b. Some go up and some go down.

1$36 bike, losing $12 a yeary =x

236% battery, 6% an houry =x

360 km to go, 3 km an houry =x

4$20 to hire, then $8 a miley =x

518 °C, rising 3 °C a minutey =x

615 bricks laid, 3 an houry =x

7$20 delivery, $2 an itemy =x

8$12 call-out, then $5 an houry =x

What the numbers in a rule meanStarts and rates

Name: Date:

Read what each rule says about the situation, then answer the question.

1y = −8x + 30 — kilograms of feed left after x daysHow much is used each day?

2y = 8x + 24 — height of a plant in cm after x weeksHow tall was it to start?

3y = 5x + 25 — phone bill in dollars after x GBWhat does each GB cost?

4y = −4x + 20 — kilograms of feed left after x daysHow much feed was there to start?

5y = 3x + 30 — pages read after x daysHow many were read already?

6y = 5x + 50 — cost of a gym for x monthsWhat does each month cost?

7y = −2x + 15 — temperature in °C after x hoursHow warm was it to start?

8y = −8x + 45 — stock left after x daysHow many were in stock to start?

Transformations of a functionShifts, stretches and reflections

Name: Date:

Circle what happens to the graph of f to give the graph of g.

1f(x) = x³, g(x) = (x + 5)³LeftRightUpDownStretchShrinkReflect

2f(x) = x², g(x) = (x − 3)²LeftRightUpDownStretchShrinkReflect

3f(x) = x², g(x) = −x²LeftRightUpDownStretchShrinkReflect

4f(x) = x², g(x) = 0.25x²LeftRightUpDownStretchShrinkReflect

5f(x) = √x, g(x) = √x + 2LeftRightUpDownStretchShrinkReflect

6f(x) = |x|, g(x) = |x| − 5LeftRightUpDownStretchShrinkReflect

7f(x) = |x|, g(x) = |x + 5|LeftRightUpDownStretchShrinkReflect

8f(x) = |x|, g(x) = 4|x|LeftRightUpDownStretchShrinkReflect

Parallel and perpendicular linesBoth, mixed

Name: Date:

Write the equation of the line through each point. // means parallel, ⊥ means perpendicular.

1(2, −11), ⊥ x − 3y = 6

2(−1, 9), ⊥ x − 2y = −4

3(3, 15), // y = 2x + 6

4(2, −1), // y = 2x − 7

5(2, 5), ⊥ x + 2y = 4

6(2, 9), // y = 4x + 2

7(−1, 5), ⊥ x + 3y = −3

8(−1, −5), // y = −3x − 10

Power Pack · Functions and rulesAnswer key

Write the rule

1. $36 bike, losing $12 a year → y = −12x + 362. 36% battery, 6% an hour → y = −6x + 363. 60 km to go, 3 km an hour → y = −3x + 604. $20 to hire, then $8 a mile → y = 8x + 205. 18 °C, rising 3 °C a minute → y = 3x + 186. 15 bricks laid, 3 an hour → y = 3x + 157. $20 delivery, $2 an item → y = 2x + 208. $12 call-out, then $5 an hour → y = 5x + 12

What each number stands for

1. y = −8x + 30 — How much is used each day? 82. y = 8x + 24 — How tall was it to start? 243. y = 5x + 25 — What does each GB cost? 54. y = −4x + 20 — How much feed was there to start? 205. y = 3x + 30 — How many were read already? 306. y = 5x + 50 — What does each month cost? 57. y = −2x + 15 — How warm was it to start? 158. y = −8x + 45 — How many were in stock to start? 45

Transformations

1. f(x) = x³, g(x) = (x + 5)³: Left2. f(x) = x², g(x) = (x − 3)²: Right3. f(x) = x², g(x) = −x²: Reflect4. f(x) = x², g(x) = 0.25x²: Shrink5. f(x) = √x, g(x) = √x + 2: Up6. f(x) = |x|, g(x) = |x| − 5: Down7. f(x) = |x|, g(x) = |x + 5|: Left8. f(x) = |x|, g(x) = 4|x|: Stretch

Parallel and perpendicular

1. (2, −11), ⊥ x − 3y = 6 → y = −3x − 52. (−1, 9), ⊥ x − 2y = −4 → y = −2x + 73. (3, 15), // y = 2x + 6 → y = 2x + 94. (2, −1), // y = 2x − 7 → y = 2x − 55. (2, 5), ⊥ x + 2y = 4 → y = 2x + 16. (2, 9), // y = 4x + 2 → y = 4x + 17. (−1, 5), ⊥ x + 3y = −3 → y = 3x + 88. (−1, −5), // y = −3x − 10 → y = −3x − 8

Functions and rules

What is in the pack

The algebra track

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