Unit 7 Review (Functions)

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a function?

Back

The y-intercept is the value of the function when the input (x) is zero; it is the point where the graph intersects the y-axis.

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 input into the function's equation and simplify.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and can graph as curves.

Front

What is the output of the function g(x) = 3x + 6 when x = 7?

Back

The output is g(7) = 3(7) + 6 = 27.

Front

What is the output of the function g(x) = 3x + 6 when x = -4?

Back

The output is g(-4) = 3(-4) + 6 = -12 + 6 = -6.

Front

What is the output of the function f(x) = 4x - 2 when x = 5?

Back

The output is f(5) = 4(5) - 2 = 20 - 2 = 18.