Unit 1 review - modeling linear functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

In the function c(x) = 5x + 100, what does the 5 represent?

Back

In the function c(x) = 5x + 100, the 5 represents the cost per mile driven by the tow truck.

Front

What is the y-intercept in the function c(x) = 5x + 100?

Back

The y-intercept in the function c(x) = 5x + 100 is 100, which represents the flat rate charged by the tow truck before any miles are driven.

Front

How do you interpret c(40) = 300 in the context of the tow truck problem?

Back

c(40) = 300 means that if the tow truck is driven 40 miles, the total cost will be $300.

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

How do you determine the domain of the function f(t) = 400 - 16t?

Back

The domain of the function f(t) = 400 - 16t is determined by the context; in this case, it is 0 ≤ t ≤ 25, as the pool cannot have negative water or be drained beyond its capacity.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

In the context of the function f(t) = 400 - 16t, what does the constant 16 represent?

Back

In the function f(t) = 400 - 16t, the constant 16 represents the rate at which water is draining from the pool, in gallons per minute.