Evaluating Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How do you evaluate a function for a given value?

Back

To evaluate a function for a given value, substitute the value into the function's equation and simplify to find the output.

Front

What does it mean for a set of values to be a function?

Back

A set of values is a function if each input (x-value) is associated with exactly one output (y-value).

Front

Evaluate the function f(x) = 2x + 3 when x = 4.

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

Evaluate the function g(x) = x^2 - 5 when x = -3.

Back

g(-3) = (-3)^2 - 5 = 9 - 5 = 4.

Front

What is the output of the function h(x) = 3x - 7 when x = 2?

Back

h(2) = 3(2) - 7 = 6 - 7 = -1.

Front

How do you determine if a relation is a function using a graph?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

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

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

Evaluate the function f(x) = -2x + 1 when x = 10.

Back

f(10) = -2(10) + 1 = -20 + 1 = -19.