AE 7.6 Practice

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the function f(x) = mx + b.

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: f(a).

Front

What is the process to solve for x in the equation f(x) = c?

Back

To solve for x, set the function equal to c and isolate x. This may involve algebraic manipulation.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if for every x in their domain, f(x) = g(x).

Front

How do you find the composition of two functions f and g, denoted as f(g(x))?

Back

To find the composition f(g(x)), substitute g(x) into the function f wherever x appears.

Front

What is the significance of the roots of a function?

Back

The roots of a function are the values of x for which f(x) = 0. They represent the x-intercepts of the graph.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept (b) and use the slope (m) to find another point. Draw a straight line through these points.

Front

What is the formula for finding the equation of a line given two points?

Back

The equation of a line can be found using the point-slope form: y - y1 = m(x - x1), where m is the slope.