Chapter 1 Review Functions and Linear Equations

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

Define 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 does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

How do you find the average rate of change of a function on an interval [a,b]?

Back

The average rate of change of a function f on the interval [a,b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).

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 is an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

Define a linear equation.

Back

A linear equation is an equation of the form \( ax + b = 0 \), where a and b are constants and a ≠ 0.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented as (0, f(0)).

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) is associated with exactly one output (y-value).