An item is being lifted by an elevator at a constant speed to a height of 10 feet. The item does not move for five seconds then catapults off the 10-foot platform and back to the ground. Compare the height of the item to the time passed in seconds. Determine the correct types of functions that describes the scenario in the correct order.(1 point)

Question

Responses

Linear Function, Constant Function, Quadratic Function
Linear Function, Constant Function, Quadratic Function

Linear Function, Constant Function, Linear Function
Linear Function, Constant Function, Linear Function

Quadratic Function, Constant Function, Linear Function
Quadratic Function, Constant Function, Linear Function

Constant Function, Quadratic Function, Linear Function
Constant Function, Quadratic Function, Linear Function

Answer 1

To analyze the given scenario:

1. Lifting the item: While the elevator is lifting the item to a height of 10 feet at a constant speed, the height of the item as a function of time will be a linear function. This is because the height increases steadily over time.

2. Item remains at 10 feet: Once the item reaches the 10-foot platform and does not move for five seconds, the height of the item remains constant. Thus, this portion can be described by a constant function.

3. Item catapults off the platform: When the item catapults off the platform, it follows a parabolic motion as it falls to the ground. The height of the item as it descends can be described by a quadratic function, typically represented by the equation of a downward-opening parabola.

So, the correct order of functions describing the height of the item over time is:

Linear Function, Constant Function, Quadratic Function

Therefore, the correct response is:

Linear Function, Constant Function, Quadratic Function

Answer 2

What scenario can be represented by the line labeled 2 in the graph?
2 is a constant function

(1 point)
Responses

walking back toward home at a constant speed
walking back toward home at a constant speed

an object falling from a tall building
an object falling from a tall building

stopping for an animal to cross the road
stopping for an animal to cross the road

speeding up to reach top speed
speeding up to reach top speed

Answer 3

A constant function on a graph indicates that the value (in this case, height or position) remains unchanged over a certain period of time. Therefore, the scenario that best represents a constant function, where there is no change in position over time, would be:

Stopping for an animal to cross the road.

In this scenario, the person or vehicle coming to a stop creates a period where the position remains constant until the animal has crossed, resulting in a horizontal line on the graph.

The other options involve changes in position (walking, falling, or speeding up), which would not be described by a constant function.

Answer 4

What scenario could represent the pieces of function types in the graph?
its a linear, constant and quadratic in that order
(1 point)
Responses

A diver climbs to the diving board to jump.
A diver climbs to the diving board to jump.

An ultimate frisbee player throws a frisbee to score a point.
An ultimate frisbee player throws a frisbee to score a point.

An athlete goes on a run from home and then comes back home.
An athlete goes on a run from home and then comes back home.

A train ride at the fair has one stop.

Answer 5

To evaluate the scenario that fits the sequence of function types linear, constant, and quadratic, let's break down the options:

1. A diver climbs to the diving board to jump: This scenario can represent a linear function while climbing, a constant function while the diver is on the board before jumping, and then a quadratic function as they fall through the air after jumping. This aligns well with the specified types of functions.

2. An ultimate frisbee player throws a frisbee to score a point: The frisbee’s trajectory could be quadratic, but there isn't a clear linear or constant segment represented in the process of throwing.

3. An athlete goes on a run from home and then comes back home: The initial segment of the run could be linear, a constant segment can exist when they pause (if they do), but the entire process of running there and back more likely wouldn’t fit the order given.

4. A train ride at the fair has one stop: The train moves (linear), stops (constant), and then may move again (potentially linear). However, this doesn't clearly fit a quadratic function segment.

Given the explanations, the best option that matches the sequence of linear → constant → quadratic is:

A diver climbs to the diving board to jump.

This scenario effectively uses all three function types in the correct order.

Answer 6

A rectangle has a length represented by the function f(x)=x
and a width represented by the function g(x)=x+3
where both functions are in feet.

Calculate (f⋅g)(x)
and state what it represents.

(1 point)
Responses

(f⋅g)(x)=x2+3x
; It represents the area of the rectangle in square feet.
(f⋅g)(x)=x2+3x
; It represents the area of the rectangle in square feet.

(f⋅g)(x)=x2+3x
; It represents the perimeter of the rectangle in feet.
(f⋅g)(x)=x2+3x
; It represents the perimeter of the rectangle in feet.

(f⋅g)(x)=4x+6
; It represents the perimeter of the rectangle in feet.
(f⋅g)(x)=4x+6
; It represents the perimeter of the rectangle in feet.

(f⋅g)(x)=4x+6
; It represents the area of the rectangle in square feet.

Answer 7

To calculate \((f \cdot g)(x)\), we start by determining the functions for the length and width:

• The length of the rectangle is given by \(f(x) = x\).
• The width of the rectangle is given by \(g(x) = x + 3\).

Now, we can calculate \((f \cdot g)(x)\):

\[ (f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 3). \]

Next, we distribute \(x\) within the parentheses:

\[ (f \cdot g)(x) = x^2 + 3x. \]

This result, \(x^2 + 3x\), represents the area of the rectangle in square feet, since the area \(A\) of a rectangle is calculated as:

\[ A = \text{length} \times \text{width} = f(x) \cdot g(x). \]

Thus, the correct response is:

\((f \cdot g)(x) = x^2 + 3x\); It represents the area of the rectangle in square feet.

Answer 8

Given that f(x)=6x2−2x
and g(x)=2x
, what is the domain of (fg)(x)
?(1 point)
Responses

the set of all real numbers except x=0
and x=13
the set of all real numbers except x is equal to 0 and x is equal to 1 third

the set of all real numbers except x=13
the set of all real numbers except x is equal to 1 third

the set of all real numbers
the set of all real numbers

the set of all real numbers except x=0

Answer 9

To determine the domain of the product \((fg)(x)\), we need to examine the individual functions \(f(x)\) and \(g(x)\):

1. Function \(f(x) = 6x^2 - 2x\): This is a polynomial function, and polynomial functions are defined for all real numbers. Therefore, the domain of \(f(x)\) is the set of all real numbers.

2. Function \(g(x) = 2x\): This is also a polynomial function, specifically a linear one. This function is likewise defined for all real numbers. Hence, the domain of \(g(x)\) is also the set of all real numbers.

When finding the domain of the product \((fg)(x)\), we take the intersection of the domains of \(f(x)\) and \(g(x)\). Since both functions are defined for all real numbers, their product \((fg)(x)\) will also be defined for all real numbers.

Thus, the domain of \((fg)(x)\) is:

The set of all real numbers.