Function Notation and Evaluating Functions

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

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 expression and simplify.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of f(x) when given f(x) = 2x^2 + 5x - 3?

Back

Substitute the value of x into the equation and simplify to find f(x). For example, f(-1) = 2(-1)^2 + 5(-1) - 3 = -6.

Front

What is the significance of the coefficients in a quadratic function?

Back

The coefficients determine the shape and position of the parabola represented by the quadratic function. The 'a' coefficient affects the width and direction of the parabola.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as 'm' in the equation f(x) = mx + b.

Front

How do you evaluate a linear function like h(x) = -5x + 7 at a specific point?

Back

Substitute the specific value of x into the function. For example, h(2) = -5(2) + 7 = -3.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).