Evaluating Functions and Their Properties

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.

Front

Given the function f(x) = x^2 + 3, how do you evaluate f(-2)?

Back

To evaluate f(-2), substitute -2 for x: f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

Front

What does it mean to shift a function vertically?

Back

Shifting a function vertically means adding or subtracting a constant to/from the function's output (y-values). For example, f(x) + 3 shifts the graph of f(x) up by 3 units.

Front

How do you find the x-value when given f(x) = k?

Back

To find the x-value when given f(x) = k, set the function equal to k and solve for x.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input value corresponds to exactly one output value. This can be checked using the vertical line test.

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function; it is calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean to evaluate a function?

Back

Evaluating a function means substituting a specific value for the variable and calculating the output.

Front

What is the effect of doubling the slope of a linear function?

Back

Doubling the slope of a linear function makes the line steeper, increasing the rate of change.