AnswersAlgebraic ReasoningCombinations and Separations of Functions

Combinations and Separations of Functions — Quiz Answers

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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 ?

A
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'
B
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'
C
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'
D
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'
4

On a given day, the temperature in a pool increases with both the work of a heater modeled by the function h of t and the Sun s times t , depending on the amount of time that passes, t , in minutes. Which graph best shows the combination of both functions, c times t ?

A
Image with description A first-quadrant coordinate plane. On the coordinate plane, the x-axis ranges from 0 to 50 in increments of 10, and the y-axis ranges from 0 to 10 in increments of 5. The graph has 2 straight lines (h of t), and (s of t), a curve (c of t) that originate from the origin. The curve (c of t) passes close to (10 comma 2 point 5). Both (h of t) and (s of t) go to the right. The straight line (s of t) goes right and it moves close to the x-axis, and (h of t) is just above (s of t).
B
Image with description A first-quadrant coordinate plane. On the coordinate plane, the x-axis ranges from 0 to 50 in increments of 10, and the y-axis ranges from 0 to 10 in increments of 5. The graph has 3 straight lines (c of t), (h of t), and (s of t) that originate from the origin. The line (c of t) passes through (45 comma 5). Both (h of t) and (s of t) go to the right. The line (s of t) almost coincides with the x-axis, and (h of t) is just above (s of t).
C
Image with description A first-quadrant coordinate plane. On the coordinate plane, the x-axis ranges from 0 to 50 in increments of 10, and the y-axis ranges from 0 to 10 in increments of 5. The graph has 3 straight lines (c of t), (h of t), and (s of t) that originate from the origin. The line (c of t) passes close to (50 comma 10). Both (h of t) and (s of t) go to the right. The straight line (s of t) goes right, and it moves close to the x-axis, and (h of t) is just above (s of t).
D
Image with description A first-quadrant coordinate plane. On the coordinate plane, the x-axis ranges from 0 to 50 in increments of 10, and the y-axis ranges from 0 to 10 in increments of 5. The graph has 2 straight lines (h of t) and (s of t), a curve (c of t) that originate from the origin. The curve (c of t) passes close to (40 comma 2 point 5). Both (h of t) and (s of t) go to the right. The straight line (s of t) goes right, and it moves close to the x-axis, and (h of t) is just above (s of t).
5

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

A
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (h of x), a straight line (g of x), and smooth curves (f of x). The parabola (h of x) has a vertex at (0 comma negative 6) and passes close to (negative 2 point 5 comma 0). It has a hole close to (2 point 5 comma 0). The straight line (g of x) has a positive slope and passes close to (negative 2 point 5 comma 0) and (0 comma 2). One curve of (f of x) lies in the first quadrant and the other spreads in the third and fourth quadrants. The curve in the first quadrant has a horizontal asymptote at y equals 0. It goes in the positive direction of the x-axis and has a vertical asymptote at x approximately equal to 2 point 5. The other curve also has a horizontal asymptote at y equals 0, and it goes in the negative direction of the x-axis and has a vertical asymptote like the first curve.
B
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (f of x), and two straight lines (h of x), and (g of x). The parabola (f of x) that opens upwards has a vertex at (0 comma negative 6), and passes close to (negative 2 point 5 comma 0) and (2 point 5 comma 0). The straight line (h of x) has a positive slope and passes close to (2 point 5 comma 0). The straight line (g of x) also has a positive slope, and passes close to (negative 2 point 5 comma 0) and (0 comma 2).
C
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (f of x), a straight line (g of x), and smooth curves (h of x). The parabola (f of x) has a vertex at (0 comma negative 6) and passes close to (negative 2 point 5 comma 0). The straight line (g of x) has a positive slope and passes close to (negative 2 point 5 comma 0) and (0 comma 2). One curve of (h of x) lies in the first quadrant and the other spreads in the third and fourth quadrants. The curve in the first quadrant has a horizontal asymptote at y equals 0. It goes in the positive direction of the x-axis and has a vertical asymptote at x approximately equal to 2 point 5. The other curve also has a horizontal asymptote at y equals 0, and it goes in the negative direction of the x-axis and has a vertical asymptote like the first curve.
D
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (h of x), and two straight lines (f of x), and (g of x). The parabola (h of x) that open upwards has a vertex at (0 comma negative 6), and passes close to (negative 2 point 5 comma 0) and (2 point 5 comma 0). The straight line (f of x) has a positive slope and passes close to (2 point 5 comma 0). The straight line (g of x) also has a positive slope, and passes close to (negative 2 point 5 comma 0). It appears that (f of x) and (g of x) are parallel to each other.
6

The tables show the functions to calculate the costs for a master plumber, cap m times h , and an apprentice, cap A times h , depending on the number of hours, h , that it takes to complete a job. h 2 point 7 5 3 point 2 5 4 4 point 5 cap m times h 143 169 208 234 h 2 point 7 5 3 point 2 5 4 4 point 5 cap A times h 93 point 5 110 point 5 136 153 The total cost for work done by a crew of one master plumber and one apprentice is the sum of the costs for each member of the crew. Which table shows the total cost for various times worked?

A
Table with 2 columns and 5 rows.Row 1: Column 1, 'h'; Column 2, 'cap m times h plus cap A times h' Row 2: Column 1, '2 point 7 5'; Column 2, '46 point 7 5' Row 3: Column 1, '3 point 2 5'; Column 2, '55 point 2 5' Row 4: Column 1, '4'; Column 2, '68' Row 5: Column 1, '4 point 5'; Column 2, '76 point 5'
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'h'; Column 2, 'cap m times h plus cap A times h' Row 2: Column 1, '2 point 7 5'; Column 2, '239 point 2 5' Row 3: Column 1, '3 point 2 5'; Column 2, '282 point 7 5' Row 4: Column 1, '4'; Column 2, '348' Row 5: Column 1, '4 point 5'; Column 2, '391 point 5'
C
Table with 2 columns and 5 rows.Row 1: Column 1, 'h'; Column 2, 'cap m times h plus cap A times h' Row 2: Column 1, '2 point 7 5'; Column 2, '236 point 5' Row 3: Column 1, '3 point 2 5'; Column 2, '279 point 5' Row 4: Column 1, '4'; Column 2, '344' Row 5: Column 1, '4 point 5'; Column 2, '387'
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'h'; Column 2, 'cap m times h plus cap A times h' Row 2: Column 1, '2 point 7 5'; Column 2, '49 point 5' Row 3: Column 1, '3 point 2 5'; Column 2, '58 point 5' Row 4: Column 1, '4'; Column 2, '72' Row 5: Column 1, '4 point 5'; Column 2, '81'
7

An isosceles right triangle has a hypotenuse length that can be modeled with the function h of x is equal to x square root of 2 The combined length of the legs can be modeled with the function cap l times x is equal to 2 x Which function, p times x , can be used to find the perimeter of the triangle?

A
p times x is equal to 2 x square root of 2 plus 4 x
B
p times x is equal to x square root of 2 plus 4 x
C
p times x is equal to x over 2 square root of 2 plus x
D
p times x is equal to x square root of 2 plus 2 x

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