Algebra 1 Practice Part 1

Which options represent a function? Select THREE options that represent a function.

• A.

• B.

• C.

• D.

• E.

Answer explanation

Options B, C, and E represent functions as they are either graphs on a coordinate plane or mapping diagrams with numbers and arrows, showing a unique output for each input.

Which representation shows all of the solutions to the equation y = 1/2x - 3?

• A.

• B.

• C.

• D.

Answer explanation

The correct representation that shows all solutions to the equation y = 1/2x - 3 is a graph on a coordinate plane.

Answer explanation

The correct choice is c = A/2w - b as per solving the equation A = 1/2 w (b + c) for c.

What is the solution to 2x – 8(x + 1) ≤ 6(2x – 3)?

• x ≤ 2/9

• x ≥ 2/9

• x ≤ 5/9

• x ≥ 5/9

Answer explanation

To solve the inequality, simplify both sides and solve for x. The correct solution is x ≤ 2/9, as the inequality simplifies to -6x - 8 ≤ 12x - 18, which leads to x ≤ 2/9.

Tags

A1:A-REI.B.3

Fernando works between 12 and 25 hours each week. The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works. Which statement best represents the domain of this function for any given week?

• x ≥ 9.50

• the set of integers

• 12 ≤ x ≤ 25

• the set of positive numbers

Answer explanation

The correct choice is 12 ≤ x ≤ 25 because Fernando works between 12 and 25 hours each week, so the domain of the function t(x) = 9.50x is limited to that range.

Tags

IF.B.5

Which graph shows the x- and y-intercepts of the equation 3x = 7y - 21?

• Graph A

• Graph B

• Graph C

• Graph D

Answer explanation

Graph C shows the x-intercept at (-7,0) and the y-intercept at (0,3) for the equation 3x = 7y - 21.

Tags

A1:F-IF.B.5

Which graph represents the solutions to the inequality y < -2x + 1?

• Graph A

• Graph B

• Graph C

• Graph D

Answer explanation

Graph A represents the solutions to the inequality y < -2x + 1 as it lies below the line y = -2x + 1.

Tags

A1:A-REI.D.12

Devonte is purchasing a block shaped like a rectangular prism for a construction project. He knows the volume, V, and the area of the base, B, of the block. Devonte needs to be sure that the block is not too tall for his project. He wants to rearrange the formula V = Bh so that the height, h, of the block can be determined given the volume and the area of the base. Which equation should Devonte use?

• h = B / V

• h = V / B

• h = V x B

• h = V - B

Answer explanation

This is the explanation for the answer.

Tags

A1:A-CED.A.4

A right triangle has side lengths that measure 4 units, 5 units, and √41 units. Is the value of the perimeter of the triangle a rational or irrational number? Is the value of the area of the triangle a rational or irrational number? Select the appropriate words from the list to correctly complete the sentences. The value of the perimeter of the triangle is ​ (a)   number.

The value of the area of the triangle is ​ (b)   ​ number.

• an irrational
• a rational

Answer explanation

The value of the perimeter of the triangle is an irrational number because it involves the square root of 41, which is an irrational number.

The function f, where f(m) represents the amount of water, in gallons, remaining in a bathtub after m minutes of draining at a constant rate of 16 gallons per minute. Part A Complete the equation if W represents the amount of water, in gallons, in the bathtub before draining begins. Write the variables and a symbol on the lines to create a correct equation for the function. f(m) = ​

​ (a)  

• W-16m
• W+16m
• 16+W+m