Algebra I Flashcard 9 (Fall Semester Review)

Front

What is the zero of the linear function f(x) = 2x + 3?

Back

The zero of the function is the value of x that makes f(x) = 0. For f(x) = 2x + 3, set 2x + 3 = 0, which gives x = -3/2.

Front

Solve the inequality: -3 ≤ 2x - 1 ≤ 5

Back

The solution is -1 ≤ x ≤ 3.

Front

Solve the literal equation for y = 3x + 5xz for x.

Back

x = \frac{y}{3 + 5z}.

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 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

What does it mean for a function to be linear?

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 as m = \frac{y2 - y1}{x2 - x1}.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.