Math 2A - 1st Semester Review (Units 1 & 2) 2022

Front

What does it mean for a function to be decreasing over an interval?

Back

A function is decreasing over an interval if, for any two points in that interval, the function's value at the second point is less than the value at the first point.

Front

How do you determine 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. To find the domain, identify any restrictions such as division by zero or square roots of negative numbers.

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 based on its domain.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval (a, b) does not include its endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

What is the significance of the absolute value function?

Back

The absolute value function, denoted as |x|, represents the distance of x from zero on the number line, always yielding a non-negative result.

Front

How do you solve an equation involving absolute values?

Back

To solve an equation with absolute values, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

Front

What is the formula for finding the vertex of a quadratic function in standard form?

Back

For a quadratic function in the form f(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. This means that for every x in the domain, the limit as x approaches that point equals the function's value at that point.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

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

Back

To find the x-intercepts of a function, set the function equal to zero and solve for x. The solutions are the points where the graph crosses the x-axis.