Answers Mathematics IIIMathematical Modeling: Part Three

Mathematical Modeling: Part Three — Test Answers

25 verified answers

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 ?

domain: open paren negative infinity comma infinity close paren range: open paren negative infinity comma infinity close paren

domain: open paren negative 6 point 5 comma 2 point 5 close paren range: open paren negative infinity comma infinity close paren

domain: open paren negative infinity comma 1 fourth close paren range: open paren negative 4 comma infinity close paren

domain: open paren negative infinity comma infinity close paren range: open paren negative 1 point 3 comma 2 point 3 close paren

Free Preview

What is the range of open paren f circ g close paren times x ?

y is greater than 0

all real numbers except y is equal to 0

y is less than or equal to 0

all real numbers

What is the vertex of the absolute value function?

open paren 1 comma 4 close paren

open paren 4 comma negative 1 close paren

open paren 4 comma 1 close paren

open paren 1 comma negative 4 close paren

The graph represents c , the amount a phone company charges, based on m , the number of minutes the customer uses each month. If there are a maximum of 44 comma 640 minutes in a month, which equation best represents the phone company’s monthly charges?

c is equal to 15 plus 4 over m , 0 is less than m comma m is less than or equal to 44 comma 640

c is equal to 1 fourth m plus 15 , 0 is less than or equal to m comma m is less than or equal to 44 comma 640

c is equal to 15 m plus 1 fourth , 0 is less than or equal to m comma m is less than or equal to 44 comma 640

c is equal to 15 over m , 0 is less than m comma m is less than or equal to 44 comma 640

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

y is equal to negative x cubed minus 4

y is equal to x cubed minus 4

y is equal to open paren x minus 4 close paren cubed

y is equal to open paren negative x minus 4 close paren cubed

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

y is equal to the fraction with numerator 1 and denominator x plus 2 plus 3

y is equal to x cubed plus 3

y is equal to 0 point 2 to the x th power plus 3

y is equal to log x plus 3

Which piecewise relation defines a function?

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.

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.

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.

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.

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

reciprocal

exponential

quadratic

square root

Jamilla solved the inequality start absolute value x plus b end absolute value square 2 and graphed the solution as shown. Open image in full-screen view What is the value of b and the missing symbol in Jamilla’s inequality?

b is equal to negative 1 , is less than or equal to

b is equal to 1 , is less than or equal to

b is equal to negative 1 , is greater than or equal to

b is equal to 1 , is greater than or equal to

The quantity q varies inversely with the square of m and directly with the product of r and x When m is 4 and the product of r and x is 8 , q is 2 point 5 What is the constant of variation?

5 fourths

5 eighths

If f of x is equal to 3 lfloor x minus 2 rfloor , what is f of 5 point 9 ?

When p is equal to 12 , t is equal to 2 , and s is equal to 1 sixth , r is equal to 18 If r varies directly with p and inversely with the product of s and t , what is the constant of variation?

1 eighth

4 and 1 half

1 half

A store uses the expression negative 2 p plus 50 to model the number of backpacks it sells per day, where the price, p , can be anywhere from 9 dollars to 15 dollars Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue is equal to price times number of backpacks.)

12 point 5 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 5 0 dollars .

12 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 0 0 dollars .

15 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 20 point 0 0 dollars .

9 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 32 point 0 0 .

What is the solution to the inequality start absolute value 2 n plus 5 end absolute value is greater than 1 ?

n is less than negative 3 or n is greater than negative 2

n is less than 2 or n is greater than 3

2 is less than n comma n is less than 3

negative 3 is greater than n comma n is greater than negative 2

If f of x is equal to 1 over x and g of x is equal to x plus 4 , which of the following is the graph of open paren g circ f close paren times x ?

Image with description A coordinate plane with a horizontal x-axis labeled from negative 5 to 5 in increments of 1 unit and a vertical y-axis labeled from negative 7 to 3 in increments of 1 unit, with grid lines every 1 unit. The graph consists of two separate curves. The first curve extends from an upward-pointing arrow near 0 comma 3 along the vertical y-axis, decreases sharply to pass through 1 comma negative 3, and flattens out horizontally to a rightward-pointing arrow near 5 comma negative 3.8. The second curve extends from a downward-pointing arrow near 0 comma negative 7 along the vertical y-axis, increases sharply to pass through negative 1 comma negative 5, and flattens out horizontally to a leftward-pointing arrow near negative 5 comma negative 4.2.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 2 to 8 in increments of 1 unit and a vertical y-axis labeled from negative 5 to 5 in increments of 1 unit, with grid lines every 1 unit. The graph consists of two separate curves. The first curve extends from an upward-pointing arrow near 4 comma 5, decreases sharply to pass through 5 comma 1, and flattens out horizontally to a rightward-pointing arrow near 8 comma 0.5. The second curve extends from a downward-pointing arrow near 4 comma negative 5, increases sharply to pass through 3 comma negative 1, and flattens out horizontally to a leftward-pointing arrow near negative 2 comma negative 0.5.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 5 to 5 in increments of 1 unit and a vertical y-axis labeled from negative 2 to 8 in increments of 1 unit, with grid lines every 1 unit. The graph consists of two separate curves. The first curve extends from an upward-pointing arrow near 0 comma 8 along the vertical y-axis, decreases sharply to pass through 1 comma 5, and flattens out horizontally to a rightward-pointing arrow near 5 comma 4.2. The second curve extends from a downward-pointing arrow near 0 comma negative 2 along the vertical y-axis, increases sharply to pass through negative 1 comma 3, and flattens out horizontally to a leftward-pointing arrow near negative 5 comma 3.8.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 8 to 2 in increments of 1 unit and a vertical y-axis labeled from negative 4 to 5 in increments of 1 unit, with grid lines every 1 unit. The graph consists of two separate curves. The first curve extends from an upward-pointing arrow near negative 4 comma 5, decreases sharply to pass through negative 3 comma 1, and flattens out horizontally to a rightward-pointing arrow near 2 comma 0.5. The second curve extends from a downward-pointing arrow near negative 4 comma negative 5, increases sharply to pass through negative 5 comma negative 1, and flattens out horizontally to a leftward-pointing arrow near negative 8 comma negative 0.5.

A factory produces 1 comma 250 comma 000 toys each year. The number of toys is expected to increase by about 150 percent per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

n is equal to 1 point 2 5 times 2 point 5 to the t th power

n is equal to 1 point 5 t plus 1 point 2 5

n is equal to the fraction with numerator 2 point 5 times 1 point 5 and denominator t , t is not equal to 0

n is equal to 1 point 5 t squared plus 1 point 2 5

The equation of the piecewise defined function f of x is shown. What is the value of f of 1 ? f of x equals enlarged left-brace first row x squared plus 1 comma negative 4 less than or equal to x less than 1. Second row negative x squared comma 1 less than or equal to x less than 2. Third row 3 x comma x greater than or equal to 2.

f of 1 is equal to 2

f of 1 is equal to negative 1

f of 1 is equal to 3

f of 1 is equal to negative 2

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

domain: open paren negative infinity comma infinity close paren range: open paren 0 comma infinity close paren

domain: open paren 0 comma infinity close paren range: open paren 2 comma infinity close paren

domain: open paren negative infinity comma infinity close paren range: open paren 2 comma infinity close paren

domain: open paren 0 comma infinity close paren range: open paren negative infinity comma infinity close paren

The standard diameter of a golf ball is 42 point 6 7 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0 point 0 0 2 mm. Which function could represent this situation?

f of x is equal to start absolute value 42 point 6 7 minus x end absolute value

f of x is equal to 42 point 6 7 minus absolute value of x

f of x is equal to absolute value of x minus 42 point 6 7

f of x is equal to x minus absolute value of 42 point 6 7

Which statement is true about f of x is equal to negative 2 thirds start absolute value x plus 4 end absolute value minus 6 ?

The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .

The graph of f of x is a horizontal stretch of the graph of the parent function.

The graph of f of x has a domain of x is less than or equal to negative 6 .

The graph of f of x opens upward.

Did you find these answers helpful?

Mathematical Modeling: Part Three — Test Answers

More from this Course

TRY EDGENUITY HACKS