Question
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)
Responses
Quadratic Function, Constant Function, Linear Function
Quadratic Function, Constant Function, Linear Function
Linear Function, Constant Function, Linear Function
Linear Function, Constant Function, Linear Function
Linear Function, Constant Function, Quadratic Function
Linear Function, Constant Function, Quadratic Function
Constant Function, Quadratic Function, Linear Function
Use the image to answer the question.
A step-up line is plotted in a coordinate plane. Each section of the line is labeled from 1 to 4. The x-axis for time in minutes ranges from 0 to 11 in increments of 1 and the y-axis for blocks from home ranges from 0 to 18 in increments of 1.
What scenario can be represented by the line labeled 2 in the graph?
(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
speeding up to reach top speed
speeding up to reach top speed
stopping for an animal to cross the road
Use the image to answer the question.
A couple of lines and a curve are graphed on a coordinate plane. Each section is labeled from 1 to 3. The x-axis for time in seconds ranges from 0 to 14 in increments of 1 and the y-axis for height in feet ranges from 0 to 20 in increments of 1.
What scenario could represent the pieces of function types in the graph?
(1 point)
Responses
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.
A train ride at the fair has one stop.
A diver climbs to the diving board to jump.
A diver climbs to the diving board to jump.
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)=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)=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)=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)=4x+6
; It represents the area of the rectangle in square feet.
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=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
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=0
Responses
Quadratic Function, Constant Function, Linear Function
Quadratic Function, Constant Function, Linear Function
Linear Function, Constant Function, Linear Function
Linear Function, Constant Function, Linear Function
Linear Function, Constant Function, Quadratic Function
Linear Function, Constant Function, Quadratic Function
Constant Function, Quadratic Function, Linear Function
Use the image to answer the question.
A step-up line is plotted in a coordinate plane. Each section of the line is labeled from 1 to 4. The x-axis for time in minutes ranges from 0 to 11 in increments of 1 and the y-axis for blocks from home ranges from 0 to 18 in increments of 1.
What scenario can be represented by the line labeled 2 in the graph?
(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
speeding up to reach top speed
speeding up to reach top speed
stopping for an animal to cross the road
Use the image to answer the question.
A couple of lines and a curve are graphed on a coordinate plane. Each section is labeled from 1 to 3. The x-axis for time in seconds ranges from 0 to 14 in increments of 1 and the y-axis for height in feet ranges from 0 to 20 in increments of 1.
What scenario could represent the pieces of function types in the graph?
(1 point)
Responses
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.
A train ride at the fair has one stop.
A diver climbs to the diving board to jump.
A diver climbs to the diving board to jump.
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)=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)=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)=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)=4x+6
; It represents the area of the rectangle in square feet.
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=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
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=0
Answers
GPT-4o mini
Let's go through each question one by one.
1. **Lifting an item with an elevator**:
- **Scenario**: The item is lifted at a constant speed (Linear Function) until it reaches 10 feet, then it remains at that height (Constant Function) for 5 seconds, and finally (Quadratic Function) it catapults down to the ground.
- **Answer**: **Linear Function, Constant Function, Quadratic Function**
2. **Step-up line scenario**:
- **Line labeled 2** likely represents walking back toward home at a constant speed, as it suggests a linear, constant rate of movement in one direction.
- **Answer**: **walking back toward home at a constant speed**
3. **Height vs. Time graph**:
- The pieces probably represent a scenario where an athlete goes on a run (increasing height) and then returns home (decreasing height), suggesting a return journey.
- **Answer**: **An athlete goes on a run from home and then comes back home.**
4. **Calculating (f⋅g)(x)**:
- Here, `f(x)=x` and `g(x)=x+3`. The product would be:
- (f⋅g)(x) = f(x) * g(x) = x * (x + 3) = x^2 + 3x
- This represents the area of the rectangle formed by using these dimensions.
- **Answer**: **(f⋅g)(x)=x^2+3x; It represents the area of the rectangle in square feet.**
5. **Domain of (fg)(x)**:
- Given `f(x)=6x^2−2x` and `g(x)=2x`, the product (fg)(x) will not be defined where `g(x) = 0`, which occurs at `x = 0`. The quadratic doesn't impose any additional restrictions, but x=0 is crucial.
- **Answer**: **the set of all real numbers except x=0.**
If you have more questions or need further clarification on any of the answers, feel free to ask!
1. **Lifting an item with an elevator**:
- **Scenario**: The item is lifted at a constant speed (Linear Function) until it reaches 10 feet, then it remains at that height (Constant Function) for 5 seconds, and finally (Quadratic Function) it catapults down to the ground.
- **Answer**: **Linear Function, Constant Function, Quadratic Function**
2. **Step-up line scenario**:
- **Line labeled 2** likely represents walking back toward home at a constant speed, as it suggests a linear, constant rate of movement in one direction.
- **Answer**: **walking back toward home at a constant speed**
3. **Height vs. Time graph**:
- The pieces probably represent a scenario where an athlete goes on a run (increasing height) and then returns home (decreasing height), suggesting a return journey.
- **Answer**: **An athlete goes on a run from home and then comes back home.**
4. **Calculating (f⋅g)(x)**:
- Here, `f(x)=x` and `g(x)=x+3`. The product would be:
- (f⋅g)(x) = f(x) * g(x) = x * (x + 3) = x^2 + 3x
- This represents the area of the rectangle formed by using these dimensions.
- **Answer**: **(f⋅g)(x)=x^2+3x; It represents the area of the rectangle in square feet.**
5. **Domain of (fg)(x)**:
- Given `f(x)=6x^2−2x` and `g(x)=2x`, the product (fg)(x) will not be defined where `g(x) = 0`, which occurs at `x = 0`. The quadratic doesn't impose any additional restrictions, but x=0 is crucial.
- **Answer**: **the set of all real numbers except x=0.**
If you have more questions or need further clarification on any of the answers, feel free to ask!