Types of Functions Identification

Front

What is a Linear Function?

Back

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

Front

What is an Exponential Function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. The graph of an exponential function increases or decreases rapidly.

Front

What is a Quadratic Function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax^2 + bx + c, where a, b, and c are constants. Its graph is a parabola.

Front

What is an Absolute Value Function?

Back

An absolute value function is a piecewise function defined as f(x) = |x|, which outputs the non-negative value of x. Its graph forms a V shape.

Front

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

Back

A relation is 'not a function' if it does not pass the vertical line test, meaning that for at least one x-value, there are multiple corresponding y-values.

Front

What transformation occurs in the function w(x) = f(x - 7)?

Back

The transformation is a horizontal shift to the right by 7 units.

Front

What transformation occurs in the function g(x) = 2f(x)?

Back

The transformation is a vertical stretch by a factor of 2.

Front

How does multiplying a quadratic function by a negative number affect its graph?

Back

Multiplying a quadratic function by a negative number causes the graph to open downward.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upward or downward.