Algebra 1 Midterm

Front

True or false: every function is a relation.

Back

True. Every function is a specific type of relation where each input has exactly one output.

Front

What is the height of the canyon if a ball is thrown from the top and hits the floor after falling?

Back

100 feet. The height of the canyon is determined by the initial height from which the ball is thrown.

Front

If y varies inversely with x and y = 12 when x = 4, find y when x is 6.

Back

y = 8. Inverse variation means that as one variable increases, the other decreases.

Front

Solve the inequality −5(2x − 9) ≤ 20.

Back

x ≥ 2.5. This inequality can be solved by isolating x.

Front

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marco’s car towed if he received a bill for $71?

Back

12 miles. The total cost can be calculated by subtracting the service fee from the total bill and then dividing by the per mile charge.

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

Define inverse variation.

Back

Inverse variation occurs when one variable increases while the other decreases, following the relationship y = k/x, where k is a constant.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find the range of values that satisfy the inequality condition.

Front

What is the formula for calculating the total cost of a service with a base fee and a variable fee per unit?

Back

Total Cost = Base Fee + (Variable Fee per Unit × Number of Units).

Front

What is the difference between a relation and a function?

Back

A relation can have multiple outputs for a single input, while a function must have exactly one output for each input.