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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7D

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.