Algebra 1 Extra Credit for Semester Exam-Honors

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) to the run (change in x) between two points on the line.

Front

How do you calculate 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

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What does the notation -3 ≤ x ≤ 5 represent?

Back

This notation describes the domain of a function, indicating that x can take any value from -3 to 5, inclusive.

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

Find the range of the function f(x) = x^2 for x in the interval [-2, 2].

Back

The range is [0, 4] because the minimum value occurs at x=0 (f(0)=0) and the maximum at x=2 or x=-2 (f(2)=4).

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much the output (y) changes for a unit change in the input (x).

Front

If a line has a slope of -1/4, what does this indicate about its direction?

Back

A slope of -1/4 indicates that for every 4 units the line moves to the right (positive x-direction), it moves down 1 unit (negative y-direction), showing a downward slope.

Front

What is the difference between domain and range?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if the slope is positive (m > 0) and decreasing if the slope is negative (m < 0).