Math 1A - Module 5 Review

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is calculated as the change in the function's value divided by the change in the input value. For example, if a climber's altitude changes from 400 feet to 700 feet over 4 hours, the average rate of change is \( \frac{700 - 400}{6 - 2} = 75 \) feet per hour.

Front

How do you find the x-intercept of a line?

Back

The x-intercept of a line is found by setting the y-value to zero and solving for x. For example, if the equation of the line is \( y = 2x - 2 \), setting \( y = 0 \) gives \( 0 = 2x - 2 \) which simplifies to \( x = 1 \).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness and is calculated as the change in y divided by the change in x (rise over run). For example, if a line passes through the points (1, 2) and (3, 4), the slope is \( \frac{4 - 2}{3 - 1} = 1 \).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form \( y = mx + b \), where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases. This means the line is slanting downwards from left to right.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases. This means the line is slanting upwards from left to right.

Front

What is zero slope?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

What is an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning the x-value does not change while the y-value does.

Front

How do you calculate the average rate of change?

Back

To calculate the average rate of change, use the formula \( \frac{f(b) - f(a)}{b - a} \), where f(b) and f(a) are the function values at points b and a, respectively.