Algebra 2 Honors: Functions and Their Properties

These flashcards cover key concepts, definitions, and problems related to functions as studied in the Algebra 2 Honors course.

What defines a function?

A relation where each input is associated with exactly one output.

Is the set {(1, 2), (1, 4), (5, 5), (6, 4)} a function?

No, because the input '1' is associated with two different outputs (2 and 4).

What is the range of the function f(x) = 4x + 5 when evaluating f(6)?

49

Explain how to determine the domain of the function g(x) = √(x - 4).

Set the inside of the square root greater than or equal to zero, x - 4 ≥ 0, so the domain is [4, ∞).

What does increasing, decreasing, and constant intervals represent in a function's graph?

Increasing intervals where output rises as input increases, decreasing where output falls, and constant where output remains the same.

For the piecewise function f(x) = {3x + 5, x < -2; 4x + 7, x ≥ -2}, evaluate f(-5).

f(-5) = 3(-5) + 5 = -15 + 5 = -10.

How is the domain expressed in interval notation for a function graph including all real numbers from -3 to 2?

[-3, 2]

What is the output of the function h(x) = x^2 - 1 when x = 2?

h(2) = 2^2 - 1 = 4 - 1 = 3.

What is one method to check if a relation is a function using a graph?

The vertical line test; if any vertical line intersects the graph more than once, it is not a function.

What transformation occurs in the graph y = -|x|?

It reflects the graph of y = |x| across the x-axis.

Evaluate the absolute value equation |x + 1| = 2 and find solutions.

x + 1 = 2 or x + 1 = -2, so x = 1 or x = -3.

Determine the range for the square root function y = √(2x + 3).

[0, ∞) since the square root cannot produce negative values.