Algebra 1 Unit 4 End Test Prep

Front

What are inverse functions?

Back

Inverse functions are functions that 'reverse' the effect of the original function. If the function f takes an input x and produces an output y, then the inverse function f⁻¹ takes y as input and produces x as output.

Front

How do you determine if two functions are inverses of each other?

Back

To determine if two functions are inverses, you can choose a value for x in the first function, find the output, and then see if that output is the input for the second function. If it is, they are inverses.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does the function C(x) = 8x represent in the context of buying movie tickets?

Back

C(x) represents the total cost of buying x tickets, where each ticket costs $8.

Front

If a function calculates the area of a circle as a function of its radius, what does its inverse calculate?

Back

The inverse calculates the radius of the circle as a function of its area.

Front

How do you find the inverse of a function given in the form y = mx + b?

Back

To find the inverse, swap x and y, then solve for y. For example, for y = 3x, the inverse is x = 3y, which simplifies to y = x/3.

Front

What is the significance of the range being expressed as 'only multiples of 6'?

Back

This means that the output values (revenue) can only take on values that are multiples of 6, reflecting the cost of each ticket.

Front

What is the maximum number of tickets that can be sold if the stadium seats 2,000 people?

Back

The maximum number of tickets that can be sold is 2,000, as that is the seating capacity of the stadium.

Front

What is the relationship between the domain and the range of a function?

Back

The domain consists of all possible inputs, while the range consists of all possible outputs. The values in the range depend on the values in the domain.