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What are the domain and range of the piecewise function?

domain: x is greater than or equal to negative 3 range: y is greater than negative 6

domain: x is greater than negative 6 range: y is greater than or equal to negative 3

domain: negative 6 is less than x comma x is less than negative 2 or x is greater than negative 2 range: negative 3 is less than or equal to y comma y is less than or equal to 1 or 4 is less than y comma y is less than 8

domain: negative 3 is less than or equal to x comma x is less than or equal to 1 or 4 is less than x comma x is less than 8 range: negative 6 is less than y comma y is less than negative 2 or y is greater than negative 2

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What are the slope and y -intercept of the linear function graphed?

slope: negative 1 half ; y -intercept: 1

slope: negative 2 ; y -intercept: 2

slope: 1 half ; y -intercept: 2

slope: 2 ; y -intercept: 1

Which value could replace q on the chart?

108

108 minus n

21 minus n

Which equation represents h of x ?

h of x is equal to g of x over f of x

h of x is equal to g of x minus f of x

h of x is equal to f of x over g of x

h of x is equal to f of x minus g of x

The table shows the functions representing the height and base of a cone for different values of x x Height f of x is equal to 2 x Area of Base g of x is equal to pi x squared 1 2 pi 2 4 4 pi 3 6 9 pi 4 8 16 pi The volume of the cone when x is equal to 3 is 18 pi Which equation can be used to represent the volume of the cone, cap v times x ?

cap v times x is equal to 3 open paren f plus g close paren x

cap v times x is equal to 1 third open paren f plus g close paren x

cap v times x is equal to 1 third open paren f times g close paren x

cap v times x is equal to 3 open paren f times g close paren x

What is the solution to the equation 7 times open paren A minus 10 close paren is equal to 13 minus 2 times open paren 2 A plus 3 close paren ?

A is equal to 621

A is equal to 89 over 11

A is equal to 7

A is equal to 26 over 11

Read the word problem. Antonio has a total of 55 marbles. He has 15 green marbles and 12 red marbles. The rest of the marbles are blue. How many blue marbles does he have? A student represents the number of blue marbles as the variable b and solves this problem by writing an equation. Which strategy could help check the student’s answer?

Check that the difference of 55 and b is 15 .

Check that the sum of the b , 27 , and 15 is 55 .

Check that the difference of 55 and b is 12 .

Check that the sum of b , 12 , and 15 is 55 .

If f of x is equal to negative x squared plus 3 x plus 5 and g of x is equal to x squared plus 2 x , which graph shows the graph of open paren f plus g close paren of x ?

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A line is shown. The line crosses the y-axis near y equals 6 and slopes upward from left to right. Arrowheads at both ends indicate the line continues beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A downward-opening curve is shown. The curve reaches a highest point at approximately (0.5 comma 5) and crosses the x-axis near x equals negative 1 and x equals 2. Arrowheads at both ends indicate the curve continues downward beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. An upward-opening curve is shown. The curve reaches a lowest point at approximately (negative 1 comma 2). Arrowheads at both ends indicate the curve continues upward beyond the displayed grid.

Image with description Coordinate plane with x- and y-axes labeled. The x-axis and y-axis range from negative 8 to 8 in increments of 2. A line is shown. The line crosses the y-axis near y equals 6 and slopes downward from left to right. Arrowheads at both ends indicate the line continues beyond the displayed grid.

Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32 percent acid. One-quarter of the solution is made up of a 20 percent acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c Which equation can be used to determine c , the unknown concentration?

3 fourths c open paren 1 fourth times 0 point 2 close paren is equal to 40 times 0 point 3 2

30 c open paren 10 times 0 point 2 close paren is equal to 40 times 0 point 3 2

30 c plus 10 times 0 point 2 is equal to 40 times 0 point 3 2

3 fourths times c plus 1 fourth times 0 point 2 is equal to 40 times 0 point 3 2

Which graph represents the function y is equal to 2 x minus 4 ?

Image with description A coordinate plane with a straight line with a positive slope. The x-axis and y-axis are labeled from negative 5 to 5 in increments of 1. The line passes through the points 1 comma negative 4 and 3 comma 4.

Image with description A coordinate plane with a straight line. A straight line with a positive slope passes through the point 0 comma negative 4 and the point 2 comma 0, rising steeply from left to right.

How many liters of glycerin should be added to 12 liters of an 8 percent glycerin solution so that the resulting solution contains 16 percent glycerin? Round the answer to the nearest hundredth if necessary. Original (L) Added (L) New (L) Amount of Glycerin 0 point 9 6 x 0 point 9 6 plus x Amount of Solution 12 x 12 plus x

1 point 1 4 liters

1 point 9 2 liters

2 point 1 0 liters

0 point 1 8 liter

Which two functions are inverses of each other?

f of x is equal to 2 x , g of x is equal to negative 1 half x

f of x is equal to x , g of x is equal to negative x

f of x is equal to negative 8 x , g of x is equal to 8 x

f of x is equal to 4 x , g of x is equal to 1 fourth x

What are the domain and range of the function f of x is equal to negative square root of x plus 3 end root minus 2 ?

domain: x is greater than or equal to negative 3 range: y is greater than or equal to negative 2

domain: x is greater than or equal to negative 3 range: y is less than or equal to negative 2

domain: negative 3 is less than or equal to x comma x is less than or equal to negative 2 range: y is greater than or equal to negative 2

domain: negative 3 is less than or equal to x comma x is less than or equal to negative 2 range: y is less than or equal to negative 2

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain. A cross-section of the road can be represented on a graph using the function f of x is equal to negative 1 two hundredth open paren x minus 16 close paren open paren x plus 16 close paren , where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet?

1 point 3

1 point 6

0 point 8

0 point 1

Which equation represents a linear function?

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

y plus 9 is equal to x times open paren x minus 1 close paren

y minus 3 is equal to y times open paren x plus 4 close paren

x plus 7 is equal to negative 4 times open paren x plus 8 close paren

Which function is a quadratic function?

h of x is equal to 3 x open paren x minus 2 close paren minus 4

p times x is equal to 2 x open paren x squared plus 6 close paren plus 1

t times x is equal to negative 8 x squared open paren x squared minus 6 close paren plus 1

m times x is equal to negative 4 times open paren x plus 3 close paren minus 2

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

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with increments of 5. The graph has a parabola g of x and two smooth curves f of x and h of x. The parabola g of x goes through the point 0 comma negative 4 and also passes close to the point negative 2 comma 1 and negative 3 comma 1. The smooth curve h of x starts from the third quadrant, intersects the x-axis and y-axis close to the point negative 1 comma 0, 0 comma 3, and moves further to the first quadrant at point 1 comma 3. The smooth curve f of x originates from the fourth quadrant, passes through the point negative 1 comma 2, 0 comma 0, negative 2 comma 0, and then moves up to the second quadrant.

Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 with increments of 5. The graph has a parabola g of x and two smooth curves f of x and h of x. The parabola g of x passes through the point 0 comma negative 4, 2 comma 1 and passes close to negative 2 comma 0 and 2 comma 0. The smooth curve h of x starts from the third quadrant, passes through 0 comma 0, and moves further to the first quadrant at point 1 comma 4. The smooth curve f of x originates from the third quadrant, passes close to the point negative negative 1 comma 0 and 0 comma 3, and moves to the first quadrant at point 2 comma 3.

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with increments of 5. The graph has a parabola g of x and two smooth curves f of x and h of x. The parabola g of x passes through the point 0 comma negative 4 and also passes close to the point negative 2 comma 0 and 2 comma 0. The smooth curve f of x starts from the third quadrant, intersects the y-axis, and moves further to the first quadrant. The smooth curve h of x originates from the third quadrant, intersects the x-axis twice, moves down, and passes through the point 0 comma negative 9. It then goes up, passes through the point negative 2 comma 0, negative 3 comma 0, 2 comma 0 and moves further up into the first quadrant.

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with increments of 5. The graph has a parabola g of x and two smooth curves f of x and h of x. The parabola g of x passes through the point 0 comma negative 4 and also passes close to the point negative 2 comma 0, and 2 comma 0. The smooth curve h of x starts from the third quadrant, passes through the point 0 comma 0, and moves further to the first quadrant. The smooth curve f of x originates from the third quadrant, passes through the point 0 comma 4, negative 1 comma 0, 2 comma 4, and moves further up to the first quadrant.

The inverse of the function f of x is equal to 1 half x plus 10 is shown. h of x is equal to 2 x minus what number What is the missing value?

The table represents Bree’s trip from her home to the library and back. On her way to the library, she travels at 6 miles per hour. On her way home, she travels at 12 miles per hour. The total travel time is 2 hours. Which equation can be used to find the distance in miles from Bree’s house to the library? Distance (mi) Rate (mph) Time (hr) Trip to Library x 6 mph x over 6 Trip to Home x 12 mph x over 12

6 times 12 is equal to x

6 plus 12 is equal to x

open paren x over 6 close paren times open paren x over 12 close paren is equal to 2

x over 6 plus x over 12 is equal to 2

If m times x is equal to x squared plus 3 and n times x is equal to 5 x plus 9 , which expression is equivalent to m n times x ?

5 x squared plus 24

5 x cubed plus 9 x squared plus 15 x plus 27

25 x squared plus 90 x plus 84

x squared plus 5 x plus 12

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