AnswersAlgebra IIMathematical Modeling

Mathematical Modeling — Test Answers

25 verified answers2 views
2
Free Preview

The function h of t is equal to negative 4 point 8 7 t squared plus 18 point 7 5 t is used to model the height of an object projected in the air, where h of t is the height in meters and t is the time in seconds. What are the domain and range of the function h of t ? Round values to the nearest hundredth.

A
domain: left bracket 0 comma 3 point 8 5 right bracket range: left bracket 0 comma 18 point 0 5 right bracket
B
domain: left parenthesis negative infinity comma 3 point 8 5 right bracket range: left bracket 0 comma 18 point 0 5 right bracket
C
domain: left parenthesis negative infinity comma 3 point 8 5 right bracket range: left bracket 1 point 9 comma 18 point 0 5 right bracket
D
domain: left bracket 0 comma 3 point 8 5 right bracket range: left bracket 1 point 9 comma 18 point 0 5 right bracket
3

How can the y -intercept of the line be interpreted?

A
The initial temperature of the water is 65 degrees.
B
The water is on the stove for an average of 3 point 7 minutes.
C
The initial temperature of the water is 3 point 7 degrees.
D
The water is on the stove for a total of 65 minutes.
4

The graph of y is equal to x cubed is transformed as shown in the graph. Which equation represents the transformed function?

A
y is equal to x cubed minus 4
B
y is equal to open paren negative x minus 4 close paren cubed
C
y is equal to negative x cubed minus 4
D
y is equal to open paren x minus 4 close paren cubed
9

Which piecewise relation defines a function?

A
y equals enlarged left-brace first row x squared comma x less than or equal to negative 2. Second row 4 comma negative 2 less than x less than or equal to 2. Third row x squared plus 1 comma x greater than or equal to 2.
B
y equals enlarged left-brace first row negative 3 x comma x less than negative 2. Second row 3 comma 0 less than or equal to x less than 4. Third row 2 x comma x greater than or equal to 4.
C
y equals enlarged left-brace first row x squared comma x less than negative 2. Second row 0 comma negative 2 less than or equal to x less than or equal to 4. Third row negative x squared comma x greater than or equal to 4.
D
y equals enlarged left-brace first row negative 3 x comma x less than negative 4. Second row 3 comma negative 5 less than x less than 1. Third row 2 x comma x greater than or equal to 1.
11

The population of a city, y , in thousands of people, measured x years after 1800 can be modeled by the regression equation y is equal to the fraction with numerator 187 point 6 and denominator 1 plus 29 point 4 e raised to the negative 0 point 0 3 x power Which statement best interprets a value in the equation?

A
The city population in 1800 was 187 comma 600 people.
B
The city population grows by 29 comma 400 people per year.
C
The limiting value of the city population is 187 comma 600 people.
D
The limiting value of the city population is 29 comma 400 people.
13

What are the domain and range of the function f of x is equal to 2 raised to the x plus 1 power ?

A
domain: open paren 0 comma infinity close paren range: open paren 2 comma infinity close paren
B
domain: open paren negative infinity comma infinity close paren range: open paren 0 comma infinity close paren
C
domain: open paren 0 comma infinity close paren range: open paren negative infinity comma infinity close paren
D
domain: open paren negative infinity comma infinity close paren range: open paren 2 comma infinity close paren
15

If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y , the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x ?

A
Image with description A graph shows age of trees (years) labeled 0 to 10 on the horizontal axis and number of blossoms labeled 0 to 500 on the vertical axis. A straight line increases from 0 to 9 years.
B
Image with description A graph shows age of trees (years) labeled 0 to 10 on the horizontal axis and number of blossoms labeled 0 to 500 on the vertical axis. A curved line increases from 0 to 8 years.
C
Image with description A graph shows age of trees (years) labeled 0 to 10 on the horizontal axis and number of blossoms labeled 0 to 500 on the vertical axis. A curved line decreases from 0 to 9 years.
D
Image with description A graph shows age of trees (years) labeled 0 to 10 on the horizontal axis and number of blossoms labeled 0 to 500 on the vertical axis. A line increases from 0 to 3 years then decreases from 3 to 7 years.
16

When graphing the function f of x is equal to negative start absolute value x plus 5 end absolute value plus 12 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?

A
Xmin: minus 5 , Xmax: 5 Ymin: minus 20 , Ymax: 20
B
Xmin: minus 10 , Xmax: 10 Ymin: minus 10, Ymax: 10
C
Xmin: minus 20 , Xmax: 20 Ymin: minus 20 , Ymax: 20
D
Xmin: minus 10 , Xmax: 10 Ymin: minus 5 , Ymax: 5
17

Which characteristic of a data set makes a linear regression model unreasonable?

A
a correlation coefficient close to negative 1
B
a slope close to 0
C
a correlation coefficient close to 0
D
a slope close to negative 1
18

Based on the family the graph belongs to, which equation could represent the graph?

A
y is equal to the fraction with numerator 1 and denominator x plus 2 plus 3
B
y is equal to x cubed plus 3
C
y is equal to 0 point 2 to the x th power plus 3
D
y is equal to log x plus 3
20

What are the domain and range of the function f of x is equal to 1 fourth times open paren x cubed plus 6 x squared plus 5 x minus 4 close paren ?

A
domain: open paren negative infinity comma infinity close paren range: open paren negative 1 point 3 comma 2 point 3 close paren
B
domain: open paren negative infinity comma infinity close paren range: open paren negative infinity comma infinity close paren
C
domain: open paren negative 6 point 5 comma 2 point 5 close paren range: open paren negative infinity comma infinity close paren
D
domain: open paren negative infinity comma 1 fourth close paren range: open paren negative 4 comma infinity close paren

Did you find these answers helpful?