Functions Review

Front

What is a function in mathematics?

Back

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

Front

What is the vertical line test?

Back

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

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input (x value) is associated with more than one output (y value).

Front

How can you determine if a set of ordered pairs represents a function?

Back

Check if any x value appears more than once in the set of ordered pairs. If it does, the relation is not a function.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the equation of a line given two points?

Back

Use the formula for slope (m = (y2 - y1) / (x2 - x1)) to find the slope, then use the point-slope form (y - y1 = m(x - x1)) to find the equation.

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b.

Front

What is a mapping in mathematics?

Back

A mapping is a relation that pairs each element of one set with an element of another set, which can be represented as ordered pairs.

Front

What does it mean for y to be a function of x?

Back

It means that for each value of x, there is exactly one corresponding value of y.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.