Functions Digital Practice

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does f(1) = 5 mean in the context of a function?

Back

It means that when the input to the function is 1, the output is 5.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the input value into the function's equation and simplify.

Front

What is the significance of the equation g(x) = 3x + 4?

Back

This equation represents a linear function where g(x) gives the total cost for x packages of bubble gum.

Front

How do you find g(8) for the function g(x) = 3x + 4?

Back

Substitute 8 into the function: g(8) = 3(8) + 4 = 24 + 4 = 28.

Front

What does it mean if a function is undefined at a certain point?

Back

It means that there is no output value for that input, often due to division by zero or other restrictions.

Front

How do you find the output of f(x) = -x + 12 when x = -2?

Back

Substitute -2 into the function: f(-2) = -(-2) + 12 = 2 + 12 = 14.

Front

What is the inverse of a function?

Back

The inverse of a function reverses the roles of inputs and outputs, such that if f(a) = b, then f^(-1)(b) = a.

Front

What is a linear function?

Back

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

Front

What does it mean to solve for x in the equation f(x) = -2?

Back

It means to find the value of x that makes the function equal to -2.