2024 Fall Final Exam Review II.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. It models growth or decay processes.

Front

What does it mean for a function to have a slope?

Back

The slope of a function represents the rate of change of the function's output value (y) with respect to its input value (x). It is calculated as the change in y divided by the change in x.

Front

How do you find the slope of a line given its equation in standard form?

Back

To find the slope from the standard form Ax + By = C, rearrange the equation into slope-intercept form (y = mx + b) where m is the slope. The slope is -A/B.

Front

What is the significance of a line being perpendicular to another line?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope m1, the other line will have a slope m2 such that m1 * m2 = -1.

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

How do you determine 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 based on its domain (input values).

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 does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase. It is decreasing if its output values fall as the input values increase.

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. It occurs when x = 0.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point x = a, substitute a into the function and simplify to find f(a).