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 represented as f(x).

Front

How do you evaluate a function at a specific value?

Back

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

Front

What does it mean to find the value of x for which f(x) = k?

Back

It means to solve the equation f(x) = k for x, where k is a constant.

Front

What is the significance of the slope in a linear function?

Back

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

Front

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

Back

To find the x-intercept, set f(x) = 0 and solve for x.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

How do you evaluate a quadratic function at a specific point?

Back

Substitute the specific point into the quadratic equation and simplify to find the output.

Front

What is the formula for the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/(2a) and k = f(h).

Front

What does it mean to evaluate the difference f(a) - f(b)?

Back

It means to calculate the outputs of the function at points a and b, then subtract the two results.

Front

How do you solve for x in a linear equation?

Back

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