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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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).

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-IF.C.7D

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.