Comparing Linear, Exponential, and Quadratic Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 an exponential function?

Back

An exponential function is a function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive number), and x is the exponent. It shows rapid growth or decay.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you identify the y-intercept of a function?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Tags

CCSS.HSF-IF.C.7A

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1, leading to rapid increase. Exponential decay occurs when the base is between 0 and 1, leading to rapid decrease.

Tags

CCSS.HSF-IF.C.8B

Front

How can you tell if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values are constant for equal intervals of x.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the y-intercept of the function f(x) = 2x + 3?

Back

The y-intercept is 3, which is the value of f(0).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3