Linear and Non-Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, defined by the equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

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

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, then the graph does not represent a function.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Given the function f(x) = 2x + 3, what is f(1)?

Back

f(1) = 2(1) + 3 = 5.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 2?

Back

The equation is y = -1x + 2.

Front

What is the output of the function f(x) = (1/3)(x + 6) when x = -6?

Back

f(-6) = (1/3)(-6 + 6) = (1/3)(0) = 0.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.