Working With Functions

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the function behaves as the input values approach positive or negative infinity. For example, if as x approaches -∞, f(x) approaches +∞, and as x approaches +∞, f(x) also approaches +∞, the end behavior can be summarized as: As x → -∞, f(x) → +∞; As x → +∞, f(x) → +∞.

Front

What transformations occur in the function f(x) = (x-3)² + 5?

Back

The function f(x) = (x-3)² + 5 represents a transformation of the basic quadratic function f(x) = x². It is shifted to the right by 3 units and up by 5 units.

Front

What is the absolute value function?

Back

The absolute value function is defined as f(x) = |x|, which outputs the non-negative value of x. It reflects negative values to positive values.

Front

What is the result of f(n) - g(n) if f(n) = x² + 1 and g(n) = 2x - 5?

Back

The result of f(n) - g(n) is x² - 2x + 6.

Front

What type of function is represented by the graph of f(x) = ∛x?

Back

The function f(x) = ∛x is a cube root function.

Front

What does the notation f(x) mean in mathematics?

Back

f(x) represents a function named 'f' evaluated at the input 'x'. It indicates the output of the function for a given value of x.

Front

How do you find the value of a function at a specific point?

Back

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

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have the form f(x) = mx + b, where m and b are constants, and their graphs are straight lines. Quadratic functions have the form f(x) = ax² + bx + c, where a, b, and c are constants, and their graphs are parabolas.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. For the function f(x) = ax² + bx + c, the vertex can be found using the formula x = -b/(2a).