Question

find the input for each function table.
5.

input (x)	$x\div4$	output (y)
		2
		4

6.

input (x)	$5x$	output (y)
		15
		20

7.

input (x)	$3x - 2$	output (y)
		7
		16
		25
		34

8.

input (x)	$3x + 3$	output (y)
		6
		9
		12
		15

1. food a pizza place sells pizzas for $7 each plus a $4 delivery charge per order. if pat orders 3 pizzas to be delivered, what will be his total cost?
2. movies a store sells used dvds for $8 each and used videotapes for $6 each. the function rule $8d + 6v$ can be used to represent the total selling price of dvds $d$ and videotapes $v$. then use the function rule to find the price of 5 dvds and 3 videotapes.

Explanation:

Problem 5

Step1: Relate y and x

$y = \frac{x}{4} \implies x = 4y$

Step2: Calculate x for y=1

$x = 4 \times 1 = 4$

Step3: Calculate x for y=2

$x = 4 \times 2 = 8$

Step4: Calculate x for y=4

$x = 4 \times 4 = 16$

Problem 6

Step1: Relate y and x

$y = 5x \implies x = \frac{y}{5}$

Step2: Calculate x for y=10

$x = \frac{10}{5} = 2$

Step3: Calculate x for y=15

$x = \frac{15}{5} = 3$

Step4: Calculate x for y=20

$x = \frac{20}{5} = 4$

Problem 7

Step1: Relate y and x

$y = 3x - 2 \implies x = \frac{y+2}{3}$

Step2: Calculate x for y=1

$x = \frac{1+2}{3} = 1$

Step3: Calculate x for y=7

$x = \frac{7+2}{3} = 3$

Step4: Calculate x for y=16

$x = \frac{16+2}{3} = 6$

Step5: Calculate x for y=25

$x = \frac{25+2}{3} = 9$

Step6: Calculate x for y=34

$x = \frac{34+2}{3} = 12$

Problem 8

Step1: Relate y and x

$y = 3x + 3 \implies x = \frac{y-3}{3}$

Step2: Calculate x for y=3

$x = \frac{3-3}{3} = 0$

Step3: Calculate x for y=6

$x = \frac{6-3}{3} = 1$

Step4: Calculate x for y=9

$x = \frac{9-3}{3} = 2$

Step5: Calculate x for y=12

$x = \frac{12-3}{3} = 3$

Step6: Calculate x for y=15

$x = \frac{15-3}{3} = 4$

Problem 9

Step1: Define cost function

Total cost $C = 7p + 4$, where $p$ = number of pizzas

Step2: Substitute p=3

$C = 7 \times 3 + 4 = 21 + 4$

Problem 10

Step1: Substitute d=5, v=3

Total price $= 8d + 6v = 8 \times 5 + 6 \times 3$

Step2: Compute the total

$= 40 + 18$

Answer:

1. Problem 5 Inputs (x): 4, 8, 16
2. Problem 6 Inputs (x): 2, 3, 4
3. Problem 7 Inputs (x): 1, 3, 6, 9, 12
4. Problem 8 Inputs (x): 0, 1, 2, 3, 4
5. Problem 9: $\$25$
6. Problem 10: $\$58$