Evaluating Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set, typically expressed as f(x).

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 expression and simplify.

Front

What does it mean to find the inverse of a function?

Back

Finding the inverse of a function means determining a new function that reverses the effect of the original function, such that if f(x) = y, then f⁻¹(y) = x.

Front

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

Back

The slope-intercept form of a linear function is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

To find the x-intercept of a function, set the output (y) to zero and solve for the input (x).

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

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 solve for x in a function equation?

Back

To solve for x in a function equation, isolate x on one side of the equation using algebraic operations.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, characterized by a constant rate of change (slope).