Log Happiness

Front

What is the equation of the transformation if the original function is f(x) and the transformation is -f(x)?

Back

The equation of the red graph is -f(x), which reflects the graph of f(x) across the x-axis.

Front

How do you solve a system of equations?

Back

To solve a system of equations, you can use substitution, elimination, or graphing methods to find the values of the variables that satisfy all equations simultaneously.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, the domain of a function that is defined for all real numbers is (-∞, ∞).

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). If an input corresponds to more than one output, it is not a function.

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions. For example, the parent function of absolute value is f(x) = |x|.

Front

How does the graph of f(x) = |x| compare to f(x) = \frac{1}{2}|x|?

Back

The graph of f(x) = \frac{1}{2}|x| gets wider compared to the parent graph f(x) = |x|.

Front

What is the difference between linear and non-linear functions?

Back

Linear functions have a constant rate of change and can be represented by a straight line, while non-linear functions do not have a constant rate of change and can be represented by curves.

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and it is decreasing if its output values fall as the input values increase.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.