Unit 6 - Study Guide (Fib or Fact Finder)

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 of the exponential (b > 0), and 'x' is the exponent. It describes growth or decay processes.

Front

What are asymptotes in the context of Exponential Functions?

Back

Asymptotes are lines that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the x-axis (y=0), indicating that the function approaches zero as x approaches negative infinity.

Front

What is a Quadratic Function?

Back

A Quadratic Function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where 'a', 'b', and 'c' are constants and 'a' is not zero.

Front

What are the intercepts of a Quadratic Function?

Back

Intercepts are points where the graph of the function crosses the axes. The x-intercepts are found by setting f(x) = 0, while the y-intercept is found by evaluating f(0).

Front

What is a Linear Function?

Back

A Linear Function is a polynomial function of degree 1, expressed in the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you find the slope of a Linear Function?

Back

The slope (m) of a linear function is calculated as the change in y divided by the change in x (rise/run) between any two points on the line.

Front

What is the significance of the y-intercept in a Linear Function?

Back

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

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 the direction of the parabola. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the difference between growth and decay in Exponential Functions?

Back

Growth occurs when the base 'b' of the exponential function is greater than 1, while decay occurs when 'b' is between 0 and 1.

Front

What is the standard form of a Quadratic Function?

Back

The standard form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.