Calculus Math Questions

Question

Good evening, please help with these questions:

(1): A company determines that the value P, in dollars, of a certain item once it goes on sale is determined by the function p (x) = 250−15x, where x represents the years that have elapsed since the date it was launched on the market. According to the information given, the price of the item, in dollars, after 6 years from its launch corresponds to: ?

(2):

 

         RELATION A                     RELATION B

From those relations, which one corresponds to a function? Both? Only Relation A? Only Relation B? None?

 

(3): The function h given by h (t) = - 5t² + 30t, describes the path of an object t seconds after it has been thrown up from the ground (the height reached by the object is measured in meters and its friction with air is not considered). According to the information given, the height reached by the object, 2 seconds after launching corresponds to how many meters?

(4): Consider the following graphical representation of the function g:

The value of g(2) corresponds to? 1? -1? 0? 2?

 

(5): Consider the following information regarding the function f (x) = - x3 + 3x2−1, with IR domain:

Consider the following propositions:

I. The value of A that completes the table for f(x) corresponds to 27.

II. The value of C that completes the table for f(x) is the same as the value of B.

From them, they are true: Only I? Only II? Both? None?

Answer 1

Hello Francisco,

For #4, answer is included. For #1, #2, #3 and #5, I include how you could approach the questions.

#1. In this problem, since you want the value 6 years after the launch:

1. replace x by 6 in the expression P(x) = 250 - 15*x,
2. do the math and that will give you the answer.

#2: For a relation to be a function:

1. the graph has to pass the Vertical Line Test
2. for a table, an x-value can only be partnered to ONE y-value. I like to say "an x can only dance with a y, but a y can dance with as many x's as it wants."

If either relation meets one of those conditions: it is a function. Otherwise, not a function.

#3. "2 seconds after launching" means in this case, t =2. So, in the function h(t) = - 5t² + 30t, replace t by 2, do the math, and you will get the corresponding height h

#4: g(2) = (output). 2 is the input, so you start at x =2. From there, you move straight up or straight down until you meet the graph of g(x) [Note: in this case, you would move straight up]. If you do it right, you meet the graph of g(x) at the location (2,1). So 2 is the input and 1 the output, which means g(2)=1.

#5: Plug each x value into the function f(x) given, and you will get numerical values for A, B and C. From there, it will become clear which propositions are true.

Cheers!