Question

1. Suppose you are saving money for a new cell phone. At week 0 you have $20 and at week 10 you have $100. If y represents the amount of money you have saved and X represents the number of weeks, find and interpret the slope of the linear equation.
1. 1/8; $8 is put away each
week.
2. 10; $10 is put away each week.
3. 8; $8 is put away each week.
4. 1/10; $10 is put away each week.

2. If a function f (x) is shifted to the left one unit, what function represent the transformation?
1.f (x+1)
2. f (x- 1)
3. f (x)+1
4. f (x)- 1

3. Let g (x) be the reflection of f (x)=x^2+5 in the x- axis. What is the function rule for g(x)?
1. g (x)=- x^2- 5
2. g (x)=x^2+5
3. g (x)=x^2- 5
4. g (x)=- x^2+5

4. What transformations change the graph f (x) to the graph g (x)? f (x)=- 7x^2 g (x)=-35x^2+5
1. The graph stretched vertically by a factor of 1/5 and slanted down 5 units
2. the graph stretched vertically by a factor of 5 and translated down 5 units.
3. the graph stretched vertically by a factor of 1/5 and translanted up 5 units.
4. the graph stretched vertically by a factor of 5 and translated up 5 units.

8. Write an equation for the following transformation of y=x a vertical stretch by a factor of 6.
1.y=6x
2. y=x/6
3. y=x+6
4. y=x-6

9. What transformations change the graph of f (x) to the graph of g (x).
1. the graph of G is the graph of f translated to the right 3 units and up 7 units.
2. the graph of G is the graph of f translated to the left 3 units and down 7 units.
3. the graph of G is the graph of f translated Up 3 units and to the left 7 units.
4. the graph of G is the graph of f translated down three units and the right 7 units.

Show your work
10. A cannery processed 1445 pounds of strawberries in 4.5 hours The Cannery processed 2320 pounds in 7 hours. write a linear equation to model the relationship between the weight of strawberries and the time too. How many pounds of strawberries can be processed in 11 hours.

11. A doctors office schedules 15 minute appointments and half hour appointments for weekdays. The doctor limits these appointments to at most 30 hours per week write an inequality to represent the number of 15 minute appointments X and the number of half hour appointments why the doctor may have in a week.

Answer 1

1. 8; $8 is put away each week. Explanation: between week 0 and week 10 $100 - $20 = $80 were saved, that means, $8 per week.

2. f(x+1). Explanation: f(x- 1) shift f(x) to the right, f(x)+1 shift f(x) upwards, f(x)-1 shift f(x) downwards

3. g (x)= -x^2 - 5. Explanation: the reflection of f(x) in the x- axis is -f(x)

4. the graph stretched vertically by a factor of 5 and translated up 5 units. Explanation: a*f(x), a > 1 will stretch the graph of f(x) vertically by a factor of a (a = 5 in this case). f(x) + b translates the graph b units up (b = 5 in this case)

8. y = 6x. Explanation: see item 4

9. f(x) and g(x) are not provided

10.

x: time, y: pounds of strawberries processed;

data: point (4.5, 1445) and point (7, 2320);

formula of a line: y = m*x + b, where m is the slope and b is the y-intercept

slope of the line: m = (y2 - y1)/(x2 - x1) where (x1, y1) and (x2, y2) are points of the line; replacing with data: m = (2320 - 1445)/(7 - 4.5) = 350;

To calculate y-intercept of the line, replace in the general formula with a known point and the slope:

y1 = m*x1 + b

1445 = 350*4.5 + b

b = 1445 - 350*4.5  = -130

linear equation: y = 350*x -130

For x = 11 hours, y = 350*11 -130 = 3720 pounds can be processed

11.

15 minutes is equal to 0.25 hours

30 minutes is equal to 0.5 hours

x: number of 15 minute appointments

y: number of 30 minute appointments

x*0.25 <= 30

x <= 30/0.25

x <= 120

The doctor may have at most 120 appointments of 15 minutes each

x*0.5 <= 30

x <= 30/0.5

x <= 60

The doctor may have at most 60 appointments of 30 minutes each

Answer 2

1.) slope = (y2 - y1)/(x2 - x1) = (100 - 20)/(10 - 0) = 80/10 = 8
Therefore, slope is 8; $8 is put away each week.

2.) Shifting f(x) one unit to the left will yeild f(x + 1)

3.) The reflection of f(x)=x^2+5 in the x- axis  will yeild f(-x) = (-x)^2 + 5 = x^2 + 5. Therefore, g(x) = x^2 + 5