A photographer charges a sitting fee of $15, and charges $4 for each 5-in. by 7 in. photograph the customer orders. The linear function can be used to calculate the customer’s cost (c) based on the number of photographs (n) purchased. How many photographs can be purchased if you cannot spend more than $50.00?
a.
No more than 7 photographs
b.
No more than 3 photographs
c.
No more than 8 photographs
d.
No more than 9 photographs

Please select the best answer from the choices provided

A
B
C
D

It’s C

The number of photographs is "No more than 8 photographs" ⇒ C

Step-by-step explanation:

The form of the linear function is y = m x + b, where

∵ The photographer charges a sitting fee of $15

- That means its a fixed amount

∴ The fixed amount = 15

∵ He charges $4 for each 5 in. by 7 in.photograph the

   customer orders

∴ The constant rate = 4

∵ The customer’s cost is c

∵ The number of photographs purchased is n

∴ The linear function is c = 4 n + 15

∵ You cannot spend more than $50

- That means c ≤ 50

∴ 4 n + 15 ≤ 50

- Subtract 15 from both sides

∴ 4 n ≤ 35

- Divide both sides by 4

∴ n ≤ 8.75

∵ The number of photographs must be integer

∵ The first integer smaller than 8.75 is 8

∴ The number of photographs is "No more than 8 photographs"

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

13.33%

say 50 oranges, then 100 apples

80 are red, 20 are yellow

total fruit = 150

20chances out of 150 for yellow

20/150 = 13.33%