Math 3 Midterm Review Unit 3

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

How do you determine continuity in piecewise functions?

Back

A piecewise function is continuous if the limits from the left and right at the point of interest are equal and equal to the function's value at that point.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then f^{-1}(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

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

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation.

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.

Front

What is the significance of the square root in functions?

Back

The square root function can only take non-negative inputs, as the square root of a negative number is not defined in the real number system.

Front

What is the difference between a linear and a non-linear function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while a non-linear function does not have a constant rate of change and can be represented by curves.