Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What is the vertical line test?

Back

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

Front

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

Back

A mapping is a function if each input (domain) is paired with exactly one output (range). If any input is paired with more than one output, it is not a function.

Front

Given f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

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

If f(x) = x^2, what is f(-3)?

Back

f(-3) = (-3)^2 = 9.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set f(x) = 0 and solve for x.

Front

If f(x) = 3x - 6, what is the x-intercept?

Back

Set 3x - 6 = 0. Solving gives x = 2. So, the x-intercept is (2, 0).