Answers Algebraic ReasoningWriting Linear Functions

Writing Linear Functions — Test Answers

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Which function is most likely graphed on the coordinate plane?

f of x is equal to 3 x minus 11

f of x is equal to negative 5 x minus 19

f of x is equal to 4 x plus 13

f of x is equal to negative 4 x plus 12

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Which graph shows h of x is equal to f of x times g of x ?

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 10 to 10 by twos with grid lines every 2 units. Three functions are plotted on the grid. A parabola labeled f of x opens upward with its vertex at 0 comma 4, containing two highlighted solid dots at negative 2 comma 8 and 1 comma 5. A line labeled g of x slopes downward from left to right, crossing the horizontal axis at the origin 0 comma 0, containing two highlighted solid dots near negative 2 comma 0.75 and 1 comma negative 0.2. A curve labeled h of x decreases from left to right, crossing the vertical axis at 0 comma 4, and intersecting g of x near 2.5 comma negative 0.5. It contains two highlighted solid dots at negative 2 comma 6 and 1 comma 3.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 10 to 12 in increments of 2. The graph has a parabola (f of x), a straight line (g of x), and a smooth curve (h of x). The parabola (f of x) has a vertex at (0 comma 4) and passes through (negative 2 comma 8) and (2 comma 8). The straight line (g of x) has a negative slope and passes through (negative 8 comma 2) and (8 comma negative 2). The smooth curve (h of x) goes through (2 comma 4), (0 comma 0), and (negative 2 comma 6) and moves down further.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 10 to 12 in increments of 2. The graph has a parabola (f of x), a straight line (g of x), and a smooth curve (h of x). The parabola (f of x) has a vertex at (0 comma 4) and passes through (negative 2 comma 8) and (2 comma 8). The straight line (g of x) has a negative slope and passes through (negative 8 comma 2) and (8 comma negative 2). The smooth curve (h of x) goes through (0 comma 4), (negative 2 comma 2), and moves down further in the fourth quadrant.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 10 to 12 in increments of 2. The graph has a parabola (f of x), a straight line (g of x), and a smooth curve (h of x). The parabola (f of x) has a vertex at (0 comma 4) and passes through (negative 2 comma 8) and (2 comma 8). The straight line (g of x) has a negative slope and passes through (negative 8 comma 2) and (8 comma negative 2). The smooth curve (h of x) goes through (negative 4 comma 12), (negative 2 comma 4), (0 comma 0), and (2 comma negative 4) and moves down further.

If f of x is equal to absolute value of x plus 9 and g of x is equal to negative 6 , which describes the range of open paren f plus g close paren of x ?

open paren f plus g close paren of x is less than or equal to 6 for all values of x

open paren f plus g close paren of x is greater than or equal to 3 for all values of x

open paren f plus g close paren of x is less than or equal to 3 for all values of x

open paren f plus g close paren of x is greater than or equal to 6 for all values of x

A salesperson earns 200 dollars a week plus a 4 percent commission on her sales. Which equation models the relationship between her sales in a given week, s , and her weekly earnings, e ?

e is equal to 4 over 100 s plus 200

e is equal to 200 s plus 4

e is equal to 4 s plus 200

e is equal to the fraction with numerator 200 s plus 4 and denominator 100

If c times x is equal to 4 x minus 2 and d times x is equal to x squared plus 5 x , what is open paren c circ d close paren times x ?

16 x squared plus 4 x minus 6

x squared plus 9 x minus 2

4 x cubed plus 18 x squared minus 10 x

4 x squared plus 20 x minus 2

If s times x is equal to 2 minus x squared and t times x is equal to 3 x , which value is equivalent to open paren s circ t close paren times negative 7 ?

negative 439

443

negative 141

153

Which function has an inverse that is also a function?

f of x is equal to start absolute value x plus 2 end absolute value

g of x is equal to 2 x minus 3

k times x is equal to negative 9 x squared

w times x is equal to negative 20

Which equation represents a nonlinear function?

3 y plus 6 times open paren 2 minus x close paren is equal to 5

2 times open paren y plus x close paren is equal to 0

x times open paren y minus 5 close paren is equal to 2

y minus 2 times open paren x plus 9 close paren is equal to 0

Consider the table of values for h of x is equal to f of x plus g of x x f of x g of x h of x is equal to f of x plus g of x 1 3 and 1 half 1 2 4 1 fourth 3 4 and 1 half 1 ninth 4 5 1 over 16 Which values complete the table for h of x ?

Table with 1 columns and 5 rows.Row 1: Column 1, 'h of x is equal to f of x plus g of x' Row 2: Column 1, '5 and 1 half' Row 3: Column 1, '6 and 1 fourth' Row 4: Column 1, '7 and 11 over 18' Row 5: Column 1, '9 and 1 over 16'

Table with 1 columns and 5 rows.Row 1: Column 1, 'h of x is equal to f of x plus g of x' Row 2: Column 1, '3 and 1 half' Row 3: Column 1, '2' Row 4: Column 1, '1 and 1 half' Row 5: Column 1, '1 and 1 fourth'

Table with 1 columns and 5 rows.Row 1: Column 1, 'h of x is equal to f of x plus g of x' Row 2: Column 1, '3 and 1 half' Row 3: Column 1, '1' Row 4: Column 1, '1 half' Row 5: Column 1, '5 over 16'

Table with 1 columns and 5 rows.Row 1: Column 1, 'h of x is equal to f of x plus g of x' Row 2: Column 1, '4 and 1 half' Row 3: Column 1, '4 and 1 fourth' Row 4: Column 1, '4 and 11 over 18' Row 5: Column 1, '5 and 1 over 16'

If f of x is equal to 1 ninth x minus 2 , what is f inverse of x ?

f inverse of x is equal to 9 x plus 18

f inverse of x is equal to 9 x plus 2

f inverse of x is equal to 1 ninth x plus 2

f inverse of x is equal to negative 2 x plus 1 ninth

If h of x is the inverse of f of x , what is the value of h of f of x ?

f of x

Which graph represents y minus 1 is equal to 2 times open paren x minus 2 close paren ?

Image with description On a coordinate plane with x and y axes marked with negative 6 to 6, there is a straight line with a positive slope passing through the points (negative 2 comma negative 5), (0 comma negative 1), (0 point 5 comma 0) and (2 comma 3).

Image with description On a coordinate plane, the x and y axes marked from negative 6 to 6, there is a straight line with a positive slope. The line passes through the y axis at (0 comma negative 3) and the x axis at (1 point 5 comma 0). It extends indefinitely, rising from the third quadrant, through the fourth, and into the first quadrant.

Image with description On a coordinate plane with x and y axes marked with negative 6 to 6, there is a straight line with a negative slope passing through the points (0 comma 4) and (2 comma 0).

Image with description On a coordinate plane, the x and y axes marked from negative 6 to 6, there is a straight line with a negative slope. The line passes through the y axis at (0 comma 2) and the x axis at (1 comma negative 1). It extends indefinitely, descending from the second quadrant, through the first, and into the fourth quadrant.

Given p is not equal to q is not equal to 0 , what is the equation of the line that passes through the points open paren negative p comma negative q close paren and open paren p comma q close paren ?

y is equal to q

y is equal to negative x

y is equal to 2 x plus open paren 2 p minus q close paren

y is equal to q over p x

A salesperson is paid a flat rate plus a fixed percentage of her sales. Last month, she sold 16 dollars comma 000 worth of goods and was paid 1 dollars comma 600 Two months ago, she had 12 dollars comma 000 in sales and was paid 1 dollars comma 400 This month she sold 11 dollars comma 000 worth of goods. How much will she be paid?

855 dollars

550 dollars

1 dollars comma 350

1 dollars comma 100

What is the equation of the line perpendicular to 2 x minus 3 y is equal to 13 that passes through the point open paren negative 6 comma 5 close paren ?

y is equal to negative 3 halves x minus 13

y is equal to negative 3 halves x minus 4

y is equal to 2 thirds x plus 9

y is equal to 2 thirds x minus 1

If f of x is equal to x plus 7 and g of x is equal to the fraction with numerator 1 and denominator x minus 13 , what is the domain of open paren f circ g close paren times x ?

start set x such that x is not equal to negative 13 end set

start set x such that x is not equal to negative 6 end set

start set x such that x is not equal to 13 end set

start set x such that x is not equal to 6 end set

A catering company uses a linear function to determine the total cost of parties. The following table shows the costs for dinner parties with varied numbers of guests. What is the cost to cater a dinner party with 90 guests? Guests Total Cost 30 315 dollars 60 555 dollars

795 dollars

945 dollars

870 dollars

720 dollars

If u times x is equal to x to the 5th power minus x to the 4th power plus x squared and v times x is equal to negative x squared , which expression is equivalent to open paren u over v close paren times x ?

x cubed minus x squared plus 1

negative x cubed plus x squared minus 1

negative x cubed plus x squared

x cubed minus x squared

If A times x is equal to 2 x minus 4 and b times x is equal to x plus 2 , which of the following expressions produces a quadratic function?

open paren A plus b close paren times x

open paren A over b close paren times x

A b times x

open paren A minus b close paren times x

The force exerted by a pulley is the sum of the tension and the force of gravity. Since a pulley is used to lift something, the force is negative. The tables show the tension, cap t times m , and the force of gravity, cap g of m , for objects of various masses, m in grams, all accelerating upward at 2 point 5 the fraction with numerator m and denominator s squared m 0 point 5 1 point 2 2 point 6 3 point 4 cap t times m 1 point 2 5 3 6 point 5 8 point 5 m 0 point 5 1 point 2 2 point 6 3 point 4 cap g of m 4 point 9 11 point 7 6 25 point 4 8 33 point 3 2 The force of the rope is equal to the negative of the sum of the rope’s tension and the force of gravity. Which table shows the values when combining the functions to find the force of the rope?

Table with 2 columns and 5 rows.Row 1: Column 1, 'm'; Column 2, 'negative cap t times m plus cap g of m' Row 2: Column 1, '0 point 5'; Column 2, '3 point 6 5' Row 3: Column 1, '1 point 2'; Column 2, '8 point 7 6' Row 4: Column 1, '2 point 6'; Column 2, '18 point 9 8' Row 5: Column 1, '3 point 4'; Column 2, '24 point 8 2'

Table with 2 columns and 5 rows.Row 1: Column 1, 'm'; Column 2, 'negative cap t times m plus cap g of m' Row 2: Column 1, '0 point 5'; Column 2, '6 point 1 5' Row 3: Column 1, '1 point 2'; Column 2, '14 point 7 6' Row 4: Column 1, '2 point 6'; Column 2, '31 point 9 8' Row 5: Column 1, '3 point 4'; Column 2, '31 point 9 8'

Table with 2 columns and 5 rows.Row 1: Column 1, 'm'; Column 2, 'negative cap t times m plus cap g of m' Row 2: Column 1, '0 point 5'; Column 2, 'negative 3 point 6 5' Row 3: Column 1, '1 point 2'; Column 2, 'negative 8 point 7 6' Row 4: Column 1, '2 point 6'; Column 2, 'negative 18 point 9 8' Row 5: Column 1, '3 point 4'; Column 2, 'negative 18 point 9 8'

Table with 2 columns and 5 rows.Row 1: Column 1, 'm'; Column 2, 'negative cap t times m plus cap g of m' Row 2: Column 1, '0 point 5'; Column 2, 'negative 6 point 1 5' Row 3: Column 1, '1 point 2'; Column 2, 'negative 14 point 7 6' Row 4: Column 1, '2 point 6'; Column 2, 'negative 31 point 9 8' Row 5: Column 1, '3 point 4'; Column 2, 'negative 41 point 8 2'

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Writing Linear Functions — Test Answers

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