1.1 Function Notation Algebraically Practice

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols. It typically uses the letter 'f' followed by parentheses containing the input variable, such 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 in place of the variable. For example, to find f(2) in f(x) = x^2 + 3, replace x with 2: f(2) = 2^2 + 3 = 7.

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 and a ≠ 0.

Front

How do you find the value of f(x) for f(x) = x^2 - 3 + 2x when x = 6?

Back

Substitute 6 into the function: f(6) = 6^2 - 3 + 2(6) = 36 - 3 + 12 = 45.

Front

What is the output of the function g(x) = (x + 3)/5 when x = -2?

Back

Substituting -2 into g(x): g(-2) = (-2 + 3)/5 = 1/5.

Front

How do you solve for x in the equation f(x) = 2x + 1 when f(x) = 16?

Back

Set the equation: 16 = 2x + 1. Subtract 1 from both sides: 15 = 2x. Then divide by 2: x = 15/2.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, which means its highest exponent is 2. It typically has a parabolic graph.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on its graph, depending on whether it opens upwards or downwards.

Front

How do you find the value of f(x) = x^2 + 7 when x = 2?

Back

Substituting 2 into the function: f(2) = 2^2 + 7 = 4 + 7 = 11.

Front

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

Back

The coefficients a, b, and c in f(x) = ax^2 + bx + c determine the shape, direction, and position of the parabola on the graph.