Algebra 1 Chapter 3 Review

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm'. It is calculated as the ratio of the rise (change in y) over the run (change in x).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value, calculated as (f(b) - f(a)) / (b - a).

Front

How do you determine where a function is positive or negative?

Back

A function is positive where its output (y) is greater than zero and negative where its output is less than zero. This can be found by analyzing the function's graph or solving inequalities.

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 it mean if a function is always positive?

Back

If a function is always positive, it means that for all values of x in its domain, the output (y) is greater than zero.

Front

What does it mean if a function is never negative?

Back

If a function is never negative, it means that for all values of x in its domain, the output (y) is greater than or equal to zero.

Front

How do you find the rate of change from a word problem?

Back

To find the rate of change from a word problem, identify the quantities involved, determine the change in each quantity, and apply the formula: rate of change = (change in output) / (change in input).