Comparing Functions TEST

Front

What is a function?

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

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

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change, meaning the difference between consecutive outputs (y-values) is the same for equal differences in inputs (x-values).

Front

What is the significance of the slope in a linear function?

Back

The slope (m) indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function has a variable raised to the second power, resulting in a U-shaped graph (parabola) that can open upwards or downwards depending on the sign of the leading coefficient.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How can you tell if a function is exponential growth or decay?

Back

Exponential growth occurs when the base (b) in f(x) = a * b^x is greater than 1, while exponential decay occurs when the base is between 0 and 1.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0.