AnswersAlgebraic ReasoningModeling with Functions

Modeling with Functions — Quiz Answers

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Kareem wants to write an equation for the data in the table. x y negative 3 1 eighth negative 2 1 fourth negative 1 1 half 0 1 What is the general form of the equation Kareem can use to represent the data?

A
y is equal to A b to the x th power
B
y is equal to k over x , where x is not equal to 0
C
y is equal to m x plus b
D
y is equal to A x squared plus b x plus c
3

Jordan uses a linear equation to model the data in a table. Which reasoning might Jordan have used in the decision to model the data with a linear equation?

A
The y -values are the reciprocals of the corresponding x -values.
B
The change in y -values is constant for evenly spaced x -values.
C
The products of corresponding x - and y -values are equal.
D
The ratios of consecutive y -values are equal for evenly spaced x -values.
4

A travel agency made the table to represent the profits it makes on a certain vacation package. Number of People vs. Profit Number of People Who Buy the Package, x Profit per Person (in dollars), y 10 500 20 800 30 900 40 800 50 500 Which of the following explains the best model for the data in the table?

A
an absolute value function since the values increase and then decrease
B
a linear function since the profit per person changes by 30 dollars for each additional person
C
an exponential function since the ratios of the y -values are about the same
D
a quadratic function since the points lie on a curve that is symmetric about the line x is equal to 30
7

A rectangle with constant area has possible lengths and widths as shown in the table. Width vs. Length of a Rectangle Width w Length l 2 37 point 5 4 18 point 7 5 6 12 point 5 8 9 point 3 7 5 Which equation can be used to find any corresponding length and width that fit the pattern in this table?

A
l is equal to k over w , where l is the length, w is the width, and k is a constant open paren w is not equal to 0 close paren
B
l is equal to k w raised to the 1 half power , where l is the length, w is the width, and k is a constant
C
l is equal to m w plus b , where l is the length, w is the width, and m and b are constants
D
l is equal to A w squared , where l is the length, w is the width, and A is a constant
8

A science teacher wrote the table of values. Amount of Hydrogen vs. pH Amount of Hydrogen, x (in moles per liter) pH, f of x 1 tenth 1 1 over 100 2 the fraction with numerator 1 and denominator 1 comma 000 3 the fraction with numerator 1 and denominator 10 comma 000 4 the fraction with numerator 1 and denominator 100 comma 000 5 Which function models the data in the table?

A
f of x is equal to log the fraction with numerator 1 and denominator x squared , x is not equal to 0
B
f of x is equal to log 1 over x , x is not equal to 0
C
f of x is equal to the fraction with numerator 1 and denominator x squared , x is not equal to 0
D
f of x is equal to 1 over x , x is not equal to 0

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