Graded - Function Families

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 polynomial function of degree 2, typically in the form f(x) = ax^2 + 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 the base (a positive real number), and x is the exponent. Its graph shows rapid growth or decay.

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 is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions based on the input value. It can have different formulas for different intervals of the domain.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight-line graph, which has a constant slope and does not curve.

Front

What characteristics define a quadratic function's graph?

Back

A quadratic function's graph is a parabola that opens upwards or downwards, depending on the sign of the leading coefficient (a). It has a vertex, axis of symmetry, and may intersect the x-axis at two points, one point, or not at all.

Front

What are the key features of an exponential function's graph?

Back

The graph of an exponential function shows rapid growth or decay, has a horizontal asymptote, and does not intersect the x-axis (for a > 0). It increases or decreases exponentially.

Front

What is the general form of a linear absolute value function?

Back

The general form of a linear absolute value function is f(x) = a|bx + c| + d, where a, b, c, and d are constants. The graph forms a V-shape.

Front

How do you determine if a function is piecewise?

Back

To determine if a function is piecewise, check if it is defined by different expressions for different intervals of the input values. Each piece has its own formula.