Functions and Inequality Review

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. For example, in the function f(x) = 2x + 3, for every value of x, there is one corresponding value of f(x).

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. For example, 3 < 5 is an inequality.

Front

How do you solve the inequality -8(m + 2) < 4(5 + 2m)?

Back

First, distribute: -8m - 16 < 20 + 8m. Then, combine like terms: -16 < 20 + 16m. Finally, isolate m to find the solution.

Front

What does it mean for a line to be increasing?

Back

A line is increasing when, as you move from left to right, the y-values increase. This means that for any two points on the line, if the x-value of the first point is less than the x-value of the second point, the y-value of the first point is less than the y-value of the second point.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, then the graph is not a function.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation. For example, for f(x) = 1/2x + 5, to find f(11), substitute 11 for x: f(11) = 1/2(11) + 5 = 10.5.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true. For example, for the inequality 6 - 2h > 30, the solution set includes all values of h that satisfy the inequality.

Front

What does it mean when a function is linear?

Back

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

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run). For example, in the line equation y = 2x + 1, the slope is 2.

Front

What is a solution to an inequality?

Back

A solution to an inequality is a value that makes the inequality true. For example, in the inequality x > 3, any number greater than 3 is a solution.