Algebra Semester 1 Review

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. For example, for the function f(x) = x^2, the range is [0, ∞) because the output is always non-negative.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents how much the output (y) changes for a unit change in the input (x). It is calculated as the change in y divided by the change in x.

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. For example, for the function f(x) = 1/x, the domain is all real numbers except x = 0.

Front

How do you represent an inequality on a number line?

Back

An inequality can be represented on a number line by shading the region that satisfies the inequality. For example, for x < 4, you would shade to the left of 4 and place an open circle at 4.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, the inequality sign flips. For example, if -12y < -24, dividing by -12 gives y > 2.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to identify the slope and y-intercept directly.

Front

What does it mean for a function to be non-linear?

Back

A non-linear function is a function that does not create a straight line when graphed. This means the rate of change is not constant, and the function may include curves or bends.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set y = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.