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 determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If a vertical line intersects the graph at more than one point, then the relation is not a function.

Front

What does it mean to evaluate a function at a specific value?

Back

Evaluating a function at a specific value means substituting that value into the function's equation to find the corresponding output.

Front

Given f(x) = -4x - 10, how do you find f(4)?

Back

To find f(4), substitute 4 for x in the equation: f(4) = -4(4) - 10 = -16 - 10 = -26.

Front

What is the output of f(x) = -4x - 10 when f(x) = 10?

Back

To find x when f(x) = 10, set the equation -4x - 10 = 10 and solve for x: -4x = 20, x = -5.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. Each input must correspond to exactly one output.

Front

What is the definition of a mapping in mathematics?

Back

A mapping is a relation that assigns each element from one set to exactly one element in another set.

Front

What is the significance of ordered pairs in functions?

Back

Ordered pairs (x, y) represent the relationship between inputs and outputs in a function, where x is the input and y is the output.

Front

How can you identify a function from a set of ordered pairs?

Back

To identify a function from a set of ordered pairs, check that no x-value is repeated with different y-values.